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    Factors Affecting Sonic Quality of Mid & HF Horns & Waveguides

    Factors Affecting Sonic Quality of Mid & HF Horns & Waveguides (Part #1 of 9)

    This thread is an offshoot of the Handmade Ersatz M9500 thread, found at: http://www.audioheritage.org/vbulletin/showthread.php?t=12390&page=3

    The thread evolved into a comparison of various horn contours, which included a pair of questions (from Rob H. and Ian Mackenzie) addressed to me. Rather than dilute the original thread with a long reply, I have opted to initiate a new thread dedicated to a discussion of the various factors which affect subjective sound quality of horns and waveguides intended for midrange and high frequency reproduction.

    In this, and subsequent posts, I will show that the goal of high quality sound reproduction using compression drivers appears achievable if sufficient attention is given to;
    - Holistic system design, including careful crossover parameters for optimum transducer integration,
    - Applying proper horn & driver equalization and frequency response tailoring,
    - Understanding the causes, and methods to attenuate, horn-honk
    - Employing wideband CD waveguides, designed to be tonally neutral,
    - And the value of using high quality transducers.

    The original question on sound quality was posted by Ian:
    Quote Originally Posted by Ian Mackenzie
    Jack, Correct me if I am wrong but what you are talking about is the sound quality of the horn itself……snip…… Ian


    Ian’s question summarized my intent correctly; my posts do concentrate on improved sound quality of horns/waveguides as a central theme. Taking a step back, I would also add that I’m probably more concerned with overall sound quality of the full reproduction system, including: source, electronics, loudspeakers and room. I view the set of equipment and components in all four of these categories as a single unified system, and the optimization of the sound quality from the whole system should be the goal of any design exercise.

    “Big Four Criteria”
    From my experience, there are four criteria which impact a reproduction systems ability to render an impression of a live performance (in order of importance):

    1) Flat frequency response, both on axis and total radiated power.
    2) Wide frequency bandwidth. (20Hz -20kHz is sufficient)
    3) Wide dynamic range, meaning realistic peak output SPL, with low electrical and mechanical noise floor.
    4) Low distortion (all forms of non-linearity)

    I’ll nickname this lofty set of goals as “the big four criteria”, for later reference. I won’t expand on any specific details of the big four criteria, because a thorough description of the quantitative measures, and measurement techniques to confirm performance would take a lot of time and space on this post. But I will mention that each time I have made an improvement in any of the big four criteria, I have subjectively noted a qualitative improvement in the sonic reproduction. For every measurable improvement I have managed on the one or more of these four criteria, I have always been rewarded with a system that sounds more realistic.

    Clearly the big four performance criteria are acoustically, mechanically and electrically all highly inter-related, and this is the primarily motivation for a holistic rather than a disjointed approach to system design. In other words, a particular transducer sub-system, such as a compression driver and horn, should be integrated into the larger reproduction system in such a way that it does not draw attention to itself, in either a good or bad way.

    I believe that the most important sonic aspect of any compression driver horn or waveguide combination is how well it can be integrated into the total system design, such that the outcome satisfies the big four performance criteria. For instance, the required performance characteristics of a horn aimed at use in a two way speaker deployed in a small well damped living room will be different from the requirement for a good mid or top unit in a fully horn loaded system of someone living in a house the size of a sports arena.

    It’s not mandatory that each system must have its own individually designed horn, as it may be entirely possible to use the exact same horn/driver in both the previously mentioned situations. What would need to change are the specific details of crossover and equalization in the two cases, so that the device in question could be best integrated with the cabinet and other transducers to achieve specific sonic performance goals. This process requires access to specific engineering performance data for the transducers, along with a systematic approach to the design work:

    A brief summary of the design steps for transducer integration:
    1) Measure (or obtain) and review the power bandwidth and distortion across the power bandwidth of each prospective transducer in the trial system design. Does each transducer provide acceptable distortion and dynamic range limits within the intended bandwidth?

    2) Will the chosen set of transducers (in the system configuration: 2, 3, or more way) provide sufficient frequency overlap between ranges above and below each preliminary crossover point? In the case of gaps, change transducers, or increase number of units and crossover bands. Can appropriate crossover frequencies and slopes be chosen to support adequate power handling, and restrict out of band distortion? In the case of a compression driver and waveguide combination, the crossover frequencies and slopes must restrict the bandwidth to operate above the cutoff frequency and below the band where diaphragm breakup causes excessive audible distortion.

    3) Measure (or obtain) and review the (on axis and power) frequency response of each transducer. Can appropriate equalization be applied while maintaining acceptable distortion and headroom? Is the equalization practical with the chosen crossover topology?

    4) Check the directivity (polar response) of each transducer at the preliminary crossover frequencies. Do the coverage patterns match correctly on either side of each crossover point? Do the crossover frequencies need to be adjusted to provide smoother directivity transition? Will the complete system provide good power response? Adjust crossover frequencies, slopes and/or change transducers to optimize.

    I’m just scratching the surface of the tip of the iceberg in terms of system design steps, but by now you are getting the idea that a particular driver/horn/EQ combination which can excel at matching the big four criteria will be much easier to use compared to a narrow band device with rough out of band distortion and poor directivity. (Common sense really). I am emphasizing the importance of transducer integration into the total system design, because small changes in the crossover frequencies, slopes, and transducer equalization can have dramatic effects on frequency response, which will impact subjective opinion on the system, or individual transducer performance.

    Compression driver attributes:
    The preceding comments could be generically applied to almost any type of transducer; however horn/driver combinations have four acoustic aspects that definitely set them apart in terms of sonic characteristic (in order from best to worst):

    a) The highest reference efficiency of any transducer type.
    b) A wider range of designs for improved directivity control, compared to cone or planar transducers (arrays excepted).
    c) Some requirement for equalization (either electrical tailoring, or by choice of horn contour).
    d) The undesirable tendency to support longitudinal (and higher order mode) internal reflections within the horn/waveguide cavity.

    High efficiency, along with high power handling can be used to build a system with prodigious peak acoustic output capability, and wide dynamic range. Careful use of constant directivity waveguides can also be used to configure a system that produces a flat frequency spectrum, and total power response in the final listening venue, however this depends on how well the compression driver & horn equalization is rendered.

    In my experience, the equalization step is probably the most critical aspect of integrating a horn/driver combination into a loudspeaker design. Even though I use a full DSP crossover, with comprehensive EQ capability, calibrated by a laptop based acoustic test and measurement system using ETF software, (along with my own white/pink noise based spatially averaged spectral analysis technique), it still takes hours and sometimes days to use EQ for optimum response tailoring.

    Errors in EQ and gain settings among and between transducers will negatively impact the sonic character of the system, moving further away from the most important goal of the big four, namely flat frequency response. Improper EQ does not necessarily mean that the horn/driver combination is at fault, it’s just that it takes time, and a certain amount of trial and error to sort out the interaction between equalization settings, crossover frequencies & slopes, and the effect on the overall frequency & phase due to the summation across the crossover overlap zone between various drivers in the system.

    end of part 1 - Jack Bouska

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    Factors Affecting Sonic Quality of Mid & HF Horns & Waveguides (Part #2 of 9)

    Horn vs. Waveguide comparisons and the importance of EQ:
    Considering the difficulty in optimizing crossover and EQ settings for a horn/driver in a given system, I maintain a healthy skepticism towards any subjective reports of “horn shootout” comparisons posted on the internet. While I have no doubt that swapping horns and drivers in a particular system will lead the listener(s) to conclude that one particular horn/driver combination dominates in sonic quality, I have my doubts about the validity of the comparison in those cases where the audition was performed by disconnecting one driver and replacing it with another (using an L-Pad or resistor divider for approximate level setting).

    From experience, I know that changing a horn, (and/or driver) generally requires a complete re-design of the crossover (passive, active, or DSP) with attention to proper EQ of the frequency response, (in the listening room). This includes adjustment of crossover frequencies and slopes to best account for any changes in bandwidth, cutoff, distortion, etc. between different driver & horn combinations. I have occasionally taken the “lazy man’s” device-swapping approach to tweeter-tasting, with only a quick RTA based level adjustment prior to auditioning and forming an opinion regarding the “winner”, only to discover later, when I had the chance to do a proper job integrating each device with the system, that the differences between devices was much less prominent, and in some cases my established opinion of the “winner” was overturned.

    Given the difficulty in re-designing the crossover (and in some cases the baffle) for each new device in a time limited “horn-tasting” session, it’s possible that a CD waveguide might be swapped into a system which originally used an exponential, Tractrix or radial horn, however without proper HF EQ, the CD waveguide would be judged as “dark” or “mid-rangey”, by comparison, leading to a bias against such devices.

    While I don’t want to discourage any forum member from trying different horns or waveguides, and reporting on the audition conclusions in subsequent posts, it would be useful to also have a description of what crossover or system modifications were used for each different horn, and if any throat coupling converters were in use, etc. I would hate to see a particular device get a bad reputation, when some other aspect of the system, such as the crossover topology may have contributed to underperformance. When the crossover and EQ are carefully adjusted for each device, it should provide a more level playing field for comparison, so that the underlying sonic character of the horn/driver can be evaluated.

    Limitations of EQ:
    Using EQ to correct & flatten frequency response leaves two additional aspects of horn/driver behavior which are both difficult to modify using electrical EQ, and only partially, and unsatisfactorily, addressed by crossover frequency selection.

    The first aspect is the horn or waveguides directivity index as a function of frequency. Essentially no amount of EQ will turn an exponential or Tractrix horn into a wideband CD device. The best that can be done is restricting the (HF) bandwidth to a range where the device does not beam too badly, however both those types of horns will always have a increasing DI (narrowing directivity) with increasing frequency (see posts #38-42 of the Handmade Ersatz M9500 thread http://www.audioheritage.org/vbulletin/showthread.php?t=12390&page=3 ).

    I will discuss CD behavior at more length in a subsequent post in this thread.

    The second aspect (unaffected by crossover) is broadband distortion. In this category, I include both nonlinear distortions (e.g.: front compression chamber induced), and objectionable tonality caused by reflections from acoustic discontinuities at the mouth or within the horn cavity.


    Horn distortion due to internal reflections: “Horn-Honk”

    Quote Originally Posted by Ian Mackenzie
    Jack, …. Snip…..Issues of driver loading, throat impedance, the horn contour and mouth termination all seem to play a role in the subjective performance whereas there are numerous biradial CD horns that have technically good dispersion but are not subjectively that great. Ian


    In addition to the criteria of flat frequency response, I believe that the second biggest influence on the subjective quality of horns or waveguides is the unpleasant phenomenon known as “horn-honk”. This has been incorrectly attributed to a variety of causes, such as compression chamber and/or throat distortion, resonances in the horn cavity or walls, and even abrupt changes of DI between cone and horn transducers in a loudspeaker system. While the previously mentioned mechanisms can contribute to poor quality sound, the real culprit behind horn-honk is caused by poor mouth termination, and/or rapid flare rate changes within a horn or waveguide. In answer to Ian’s comment on subjectively poor performance of some CD horns, I note that many of the commercial devices on the market rely on diffraction slots and abrupt internal slope breaks (flare rate changes), while also displaying poor mouth to baffle impedance matching, all of which are responsible for imposing varying levels of horn-honk to the sonic character. Unfortunately, good CD does not guarantee good sonic performance.

    In post #5 (http://audioheritage.org/vbulletin/showpost.php?p=123500&postcount=5) of my thread: DIY Axially symmetric oblate spheroid CD waveguides, in solid Oak ( http://www.audioheritage.org/vbullet...ad.php?t=12126 )
    I briefly discussed the article: "Round The Horn" by Philip Newell and Keith Holland, (Speaker Builder, 8/94, and an excerpt was included in post #34 of the Handmade Ersatz M9500 thread referenced above). Dr. Holland concludes that the poor sonic quality of many horns is attributable to internal reflections between the mouth and throat. The horn-honk caused by these internal reflections can be easily detected as a distinct tonal aberration, similar to talking through a cardboard mailing tube, or a small tunnel. (Send me private mail if you are interested in this article.)

    Addendum: Please note that in Post #5 of my oblate spheroid thread, I incorrectly described this comb filtering effect as a resonance. I apologize if I mislead anyone by my use of that misnomer, as horn-honk is not caused by an internal resonance, but rather by one or more discrete reflections, between mouth and throat. In contrast, a typical fundamental resonance mode would exhibit a response peak much lower in frequency, which even for short horns would be below 500Hz. (eg: a 13” long horn would have a resonant frequency of 250 Hz, and a 7” horn resonance would be just over 500 Hz)

    The broad-band comb filter effect, associated with horn-honk, is created by reflection, and summation of delayed signals, which are added back into the primary acoustic output of the horn (with alternating polarity). The delay & addition of any broad-band signal with itself creates a comb filtering effect, which on a log scale amplitude plot appears as a sinusoidal ripple in an otherwise smooth response. The period of this sinusoidal pattern is related to the time delay of the reflection according to the equations:
    Time period = 1 / frequency
    (This period is measured between peaks on a linear frequency scale spectral graph).

    The comb filtering effect can be band limited in the case where the internal reflections are not broad band. In Tractrix or Exponential horns, the higher frequencies beam down the center of the horn, and do not diffract or reflect from the mouth edge, and so the response ripples will be limited to the lower octaves of the horn bandwidth (which is in the human voice range, where we are quite sensitive). In the case of CD horns, if the mouth has some form of flair, or radius, the high frequencies will be presented with a better acoustic impedance match, thus limiting the reflections to the lower octaves, similar to Tractrix and exponential horns. The reflection induced ripples in the horn frequency response have the same root cause as the impedance bumps which might be observed in the first octave or two above cutoff, these are attributed to improper mouth dimension for a given flare rate, as described by David Smith in the last sidebar of:
    http://www.audioheritage.org/html/profiles/jbl/4430-35.htm

    end of part 2 - Jack Bouska

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    Factors Affecting Sonic Quality of Mid & HF Horns & Waveguides (Part #3 of 9)

    Horn-Honk simulation:
    The first image in this thread (labeled fig 1) shows a time domain representation of two wavelets (actually two distinct single sample spikes), separated in time by 1.66ms, which is about equal to a path length difference of ~56 cm between the direct arrival and it’s 1st reflection (from the horn mouth). This is a two way travel path, (mouth-throat-mouth), which would correspond to a horn length of ~28cm measured along the straight horn walls. An impedance contrast at a horn mouth creates a negative reflection co-efficient, so the reflection is inverted polarity, and scaled in amplitude to mimic the internal reflections in real horns.

    This wavelet pair can be analyzed as a classic differentiator (high pass filter), with ripple caused by constructive and destructive interference within the HF pass band. The frequency spectrum of the wavelet pair are shown in the accompanying two graphs of fig 1, the upper graph rendered with the familiar log-log scale, and the lower graph using a linear frequency scale, which simplifies detection and estimation of ripple periodicity. The simulation of a single reflection makes the disturbance in the time domain compact, which means that the corresponding duration in the frequency domain transform will be long, and indeed we observe that the ripples extend over the full bandwidth of the high-pass zone. This is characteristic of reflections, while resonances appear to have long duration in the time domain (they ring), and short duration in the frequency domain (a narrow Q peak centered on the resonant frequency). Note that the individual spectrum of either wavelet (by itself) would be a ruler flat straight line (no ripples).

    The graphs in fig 1 are useful as comparison against spectra derived from measurements of various physical horn & transducers shown later in this post.

    On a linear amplitude scale, the interference pattern would be visible as a series of deep notches, however on a log amplitude scale the notches are compressed into sinusoidal ripple. The portion of the log spectrum which exhibits the strong sinusoidal ripples can also have a second pass of Fourier transform applied, to convert the values into the Cepstral domain, which would provide a direct readout of the offending reflection on a time scale. (Not required for this simple illustration)

    Also note that reflection induced horn-honk is not amplitude dependant (like harmonic distortion), and can be heard equally clearly at low or high amplitude levels.

    The simulation in fig 1 is illustrative of the problem, but over simplified because most real world horns, typically the slot loaded CD variety, have multiple sets of abrupt flare rate changes, with variable horn mouth termination, creating reflections with different path lengths along the horizontal and vertical walls. Multiple reflections will complicate any analysis which is reliant on frequency spectra. The reflections are also difficult to detect in real world time domain plots, as the reflection time is often shorter than the coda (tail) of the primary wavelet for band limited horn loaded transducers. Dr Holland used the Cepstral domain for analysis of complicated reflection patterns; however the examples I will show later in the post can be interpreted by simple inspection of the frequency spectrum. This ripple signature of horn-honk is often seen in various commercial frequency graphs, and can be used as a good indicator of how well the horn mouth is impedance matched to free space, and/or how much horn-honk will be audible in the device.

    Practical demonstration of Horn-Honk sound:
    In post #5 of my oblate spheroid thread (link given above), I made the comment:
    “For a practical demonstration of how important good mouth termination is for neutral tonality, simply take your favorite magazine, roll it up into a conically shaped "megaphone" then hold it up to your mouth and clearly utter the phrase: "this is the sound of horn-honk", (and you will be speaking the truth).”

    Ok, a question for those among you who read that post, please raise your hands if you actually did roll up a magazine and try the experiment I suggested? Please keep your hands raised while I count…1,2,3,4…… ok got the tally. It’s zero! (I’ll wager none of you out there in web space tried this at home!)

    I don’t blame you for not trying, if I was sitting at work on my lunch break surfing the net and read a post suggesting I talk out loud through a rolled up magazine, I wouldn’t do it either. But that’s your loss, because it’s such a simple way to hear exaggerated horn-honk, and the experience might better equip you to detect this type of distortion by ear on typical horn/driver combinations.

    Still not convinced it’s worth talking through a rolled up magazine? Read on:

    Rarely do we get a chance to perform such a relatively simple physical experiment that provides so much information about sonic character of a device. Seriously, this demo is right at the top of the “simple but mandatory” tests such as rapping your knuckles on the side of a speaker enclosure to check for panel resonances, or clapping your hands in a large, live room to check for flutter echo and/or estimate mid-band RT60 time. (Both of which I assume you have done many times in the past).

    To help entice you to try, I have extended the experiment, to include a test of your own voice using both a poor and good horn mouth termination.
    The supplies you will need are:
    1) a large size magazine (I used last months HiFi News)
    2) a large bath towel (dry)
    3) sticky tape and safety pins (optional, but handy)

    For examples of the construction, see fig 2, below.

    I suggest you can try talking through the magazine megaphone both with, and without the bath towel rolled and wrapped around the horn mouth. Without the towel the horn mouth is poorly terminated, and you will hear the expected honky-horn sound. When the towel is strategically positioned just straddling the mouth (without restricting the opening), it will provide some absorption and round-over radius for the mouth, which will in turn provide a better acoustic impedance match for the mid and high frequencies. The simple addition of this “towel cowl” (amazingly) suppresses a huge amount of the audible horn-honk.

    To try this, first talk through the magazine megaphone without the towel to gain familiarity with the honk sound. Then roll up the towel and wrap it around the mouth of the magazine megaphone, try to keep the mouth from collapsing (it helps if you have three hands). While talking through the magazine horn with the towel, it will sound flat or dead at first, but if you quickly remove the towel cowling, the honk returns instantly.

    After a few trials, it will become apparent that the sound with the towel is neither dead nor flat, but rather neutral and tonally smooth, especially compared to the naked magazine megaphone. It’s quite spooky to hear such a simple apparatus sound so clear and natural on human voice. I had the opportunity to demonstrate this at the recent LLDIYHiFi pub meeting a week ago, using a rolled up jumper (sweater) in place of the towel, and the club members were astonished at the audible difference in tone with and without the mouth treatment.

    end of part 3 - Jack Bouska
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    Factors Affecting Sonic Quality of Mid & HF Horns & Waveguides (Part #4 of 9)

    Horn-Honk measurements and calibration:
    To help entice everyone to give this a try, I have decided to do the experiment for you, (just this once), in such a way that I can measure, and graphically illustrate the spectral changes. This provides a calibration dataset to study while testing the effect while using your own DIY magazine-megaphone, and towel cowl.

    In the second image of this thread: fig 2-A and fig 2-B, illustrate the rolled up magazine which is fixed in a cone shape using masking tape, along with a small computer speaker that I substituted for my own mouth and vocal cords. Fig 2-C shows the magazine horn with the bath towel that I rolled (into a long cylinder shape) and wrapped around the mouth (half on, half off). Dimensions of this apparatus are shown at the top of fig 2.

    The next three figures 3-5, show spectral analysis (log amplitude, linear frequency scales)
    Fig 3: the naked transducer,
    Fig 4: the speaker/magazine megaphone combination, and
    Fig 5: the speaker/magazine megaphone and towel cowl combination.

    Wideband white noise was used as an excitation signal, and the microphone was slowly traversed through a 6x6x6 inch volume approximately 8” in front of the horn mouth (closer for the raw speaker), to provide a modest level of spatial filtering, which attenuates some of the floor and table early reflections, so as to highlight the spectrum of the device under test. The driving amplitude and microphone gain was kept constant, although the microphone was placed closer (4”) to the raw driver than it was for the horn tests. The scale of the spectral analysis is the same for all three plots. (1 dB/division)

    Fig 3 shows the frequency spectrum of the raw driver. The graph illustrates some resonances and response aberration inherent to this transducer, and is included for baseline comparison. The driver is seen to have sufficient output in the upper octaves to be useful for this test.

    Fig 4 shows the frequency spectrum of the speaker driving the magazine megaphone. The increased level of sinusoidal ripple across the top 4-5 octaves of the amplitude spectrum is immediately apparent. This is attributed to the strong acoustic impedance contrast at the megaphone mouth, which causes a reflected wave to travel back down the megaphone, to be reflected again from the speaker (at the throat), back to the mouth. The reflected energy combines with the primary signal to form notches in the spectrum (comb filtering. This is directly comparable with the ripple seen in the graph at bottom of fig 1.

    The clarity and amplitude of the mouth reflection of this particular horn allows the comb filter notches, and associated reflection time to be obtained by direct inspection of the FFT spectral graph. In this case, the period between peaks (or troughs) along the frequency axis is approximately 600Hz.

    This 600Hz period corresponds to reflection with time T = 1/P = 1/600Hz = 1.66ms. This time corresponds to a 2 way distance of (334m/s x 0.00166 s) = 55.6cm. This distance corresponds closely with about double the axial length of the magazine megaphone.

    The graph in fig 4 clearly shows the characteristic oscillatory spectral shape associated with the distinct tonal coloration you will observe when speaking through your own version of the magazine megaphone. This graph helps you calibrate the sound you hear from the megaphone against this familiar (and common) spectral display. You can now use the rolled up magazine to train yourself to recognize what horn-honk sounds like, and you can use the graph in fig 4 to train yourself to recognize horn-honk using spectral analysis, such as frequency response graphs published by loudspeaker manufacturers.

    Based on the description of the mechanics behind the generation of horn-honk, it should be a simple matter to devise various schemes to improve the impedance match at the mouth of our magazine megaphone, in order to suppress the honk distortion. Flaring the mouth, adding a large radius, adding damping material would all work to greater or lesser degrees; however I chose to use the towel cowl because I assume the entire forum membership either has access to a towel, or could easily borrow one from a willing neighbor. When wrapped carefully around the mouth of the magazine megaphone, the towel cowl forms a partial radius, and provides some acoustic energy damping, both of which help to “soften” the abrupt impedance contrast discontinuity at the mouth.

    The measured results of the towel cowl are shown in fig 5. Notice the nearly complete suppression of ripple above 3 kHz, with weaker attenuation of ripple between 1-3 kHz. The evidence from this spectrum alone should be sufficient to convince everyone reading this post of the value in trying the magazine megaphone and towel cowl experiment at home (A gif animation is included below for ease of comparison between figs4-5)

    Comparing the two graphs in figs 4 and 5 aids in understanding the differences which can be heard between the megaphone with and without the towel. The addition of the towel audibly improves the sound from the horn, removing a huge proportion of the unpleasant honk, so reminiscent of standing in a small tunnel.

    If at this point, you want to understand more about horn-honk, I suggest you obtain a large magazine and bath towel and try this for yourself. Remember, you can’t learn to ride a bike by simply reading a book of instructions; you actually need to get on it and try. Reading this post, and viewing the graphs may benefit the visual learners among you, but trying the experiment yourself will tap into your kinesthetic learning capability, and better tune your ears into the sound of horn-honk, so that you are better able to detect, and suppress it in your own horn loaded systems.

    Criteria for suppression of Horn-Honk:
    In their speaker builder article, Newell and Holland suggest that axially symmetric horns are the best means to attenuate the sonic aberrations associated with internal reflections. I agree that a well constructed axially symmetric horn will achieve this; however that shape is not mandatory for good tonality, and rectangular shaped horns would be equally permissible, if they adhere to the following guidelines:

    a) The throat section should be unrestricted (no diffraction slots).
    b) The throat should smoothly taper into the compression driver exit aperture.
    c) The horn walls should be straight or slightly curved, without abrupt flare rate changes.
    d) The mouth requires a “bell section, lips, or curved radius” treatment, which will effectively flare out to a full 90 degrees from the horn axis, such that the final horn wall exit angle is flush with the front baffle.
    e) The horn flare should be accompanied by complementary radius of the front baffle
    f) The edges of the horn could alternately be treated with felt, acoustic foam, or any other absorbent material that would suppress the diffraction and reflection from the mouth.
    g) The axial length should be shorter than 12” (details to follow).

    The points a) through g) above could be applied to any horn or waveguide design to yield a system capable of suppressing both the acoustic impedance contrast discontinuity at the mouth and within the horn resulting in low levels of horn-honk.

    Clearly, points a) through d) are easier to achieve when constructing an axially symmetric horn, compared to a horn with a rectangular mouth. Newell and Holland tested a device called the AX2, (which appeared to be either exponential or Tractrix flair), and the midrange tonal quality of this horn was reported as nearly equal to that of a Quad electrostatic loudspeaker. The line drawing of the device showed a very wide mouth, and presumably good flare rate match into the front baffle. It seems then, that for best tonality, the contour is not important, and any of the exponential, Tractrix, oblate spheroid or conical types can yield equally low levels of horn-honk, so long as all the external and internal acoustic impedance discontinuities are minimized.

    Considerations for commercial and DIY horns and waveguides:
    Referring again to the directivity simulations in posts #38-42 of the Handmade Ersatz M9500 thread http://www.audioheritage.org/vbulletin/showthread.php?t=12390&page=3 I note that the Tractrix and exponential horn types exhibit strong narrowing of directivity with increasing frequency, (beaming). This means that only the frequencies in the lower range, with wavelengths comparable to the axial length of the horn, will diffract enough to engage the impedance discontinuity at the horn mouth. This may contribute to the generally good quality of sound (low level of horn honk) from the Tractrix flair type, and perhaps also in exponential horns with very wide mouths, where the final exit angle approaches 90°. Horns which are truncated in axial length will exhibit much higher levels of horn-honk.

    Commercial horns or waveguides intended for PA use, (in single or multiple array configurations), tend to have rectangular shaped mouths, allowing piecewise continuity of coverage for large venues. The home constructor can be less concerned with the need to specify different coverage angles in horizontal and vertical axes, and is free to build axially symmetric contours, which can be easily turned on a home workshop lathe. The axially symmetric coverage pattern is acceptable in a home setting, where the floor is generally carpeted, and for seated listeners, the ceiling is high enough above the horn and ear height so that the first reflection from the ceiling will bounce down to a point behind the listener, if seated in the front half of the room (near the speakers)

    end of part 4 - Jack Bouska
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    Factors Affecting Sonic Quality of Mid & HF Horns & Waveguides (Part #5 of 9)

    Mouth termination in commercial horns and waveguides:
    Commercial horns and waveguides may also suffer from physical constraints associated with the need to be economical in terms of front baffle real estate. The requirement to provide good mouth termination, by either flaring the contour to 90° at the horn mouth, or providing a ¼ round radius edge around the horn/waveguide exit, mandates that the horn mouth might need to double in diameter. Earl Geddes states that the radius curve should be equal to ¼ wavelength at the lower cutoff frequency. For a 1.1 kHz cutoff, this adds almost 3” all the way around the horn mouth. Commercial horns often have cutoff frequency in the range of 550 Hz, requiring about 5” additional mouth radius, which could mean as much as 500% increase to the total front mounting surface area of a typical commercial horn. For example: a 7” x 7” horn with cutoff of 550 Hz and mouth area of 1/3 sq.ft. will require approximately an extra 5” wide radius edge around the periphery, making the final mouth area = 17” x 17” , which equals 2 sq.ft.! The size increase would not be very conducive to sales, especially if the horns are to be used in tight packed flying clusters or arrays. In practice, most commercial horns opt for compact size over good mouth termination, which is why horn-honk is still prevalent in commercial horn and waveguide offerings.

    It may be possible to modify the mouth termination of some commercial offerings to improve the tonal quality; however this should be accompanied by careful before-and-after testing and auditioning in order to verify the expected performance improvement. For internally generated reflections, modification is unlikely to improve the sound. For most DIY’ers the effort and complexity required to add a rounded cowl to the front of a commercial horn would justify building a new waveguide from scratch instead.

    Horn length impacts detectability of Horn-Honk:
    The blind testing, and subsequent analysis, of Newell and Holland also revealed that the time delay of the reflections was at least as important as the amplitude. In other words, short horns (less than 12” long) with poor mouth termination sounded better than long horns (longer than a foot) which had slightly lower amplitude reflections. This finding would encourage prospective builders to keep their waveguides as short as feasible in the axial direction.

    Human hearing is very sensitive to the time span between short period echoes. This is an important mechanism employed by our hearing system for spatial location of sound sources. Frequency response ripples (notches) are generated by directionally dependant reflection interference caused when a wave front reflects from the folds (pinnia) of the ear. Sounds impinging on the ear from different directions will illuminate different parts of the ear, changing the combination, and delay times of the resultant reflections. The sound reflected from the pinnia interferes with the direct arrival sound within the ear (at the eardrum) and the interference is detected in the cochlea as a series of notches, periodically spaced in frequency. The physical size of the ear, and the size, shape and spacing of the folds dictate that the frequencies of importance for spatial location fall in the 2khz to 6khz range.

    As evidence of our keen ability to recognize slight reflection timing differences, another simple experiment using cardboard tubes can be performed. These commonly available (bathroom roll) cardboard tubes (approximately 4” long by 1 7/8“diameter) are also illustrated in fig 1 D. After obtaining a pair of these, try cutting 1” off the end of one of them and speak through the tubes, switching lengths as you talk. Although intuition may guide otherwise, the difference between the tonalities of the two tubes is clearly audible, and although the tube lengths differ by only 1”, sonic preference goes to the shorter device. While swapping and talking, you can also try to put the two tubes end to end, and continue to speak through them both. This imparts an even more objectionable tone to the sound, yielding more horn-honk. The only variable in this experiment is the length of the tube, as all three cases have exactly the same level of acoustic impedance mis-match at the mouth, and the same loading property at the throat (your mouth). This experiment reinforces the notion that shorter horns will sound better than long ones.

    Some Horn-Honk is present in all horns and waveguides:
    The problems of mouth induced, or internally generated, reflections is a common problem among all horns and waveguides, professional or DIY alike, because the impedance matching between transducer and horn, and the horn and the room is never perfect. The best approach would be to build horns or waveguides following the guidelines in a) through f) above, followed with careful measurement and audition to ensure that horn-honk is kept to a minimum. For commercial horns or CD waveguides which exhibit honk, replacement with a better design is the best option for home use.

    As an example of how prevalent these internal reflections are in commercial devices, I include frequency response graphs from a pair of JBL speakers, which I happened to have handy. These are shown in the top part of fig 6, images: A & D. Both these graphs show clear ripple in the high frequency response. It’s a bit hard to see the periodicity because of the log frequency scale, but the time period for both graphs falls in the 600-800 Hz range, yielding a path length difference of 16 to 22 inches (corresponding to horn sidewall lengths of 8 and 11 inches). The ripple amplitude is fairly large; however the horn length falls under the magic 1 foot specification given by Newell and Holland. I have not auditioned these speakers myself, however early reports of the DD66000 sonic character are universally favorable. Despite this, the graphs don’t lie, and I suspect a critical listener would be able to detect some level of horn-honk in both devices.

    To my knowledge, the work of Dr. Holland has not received widespread attention in either of the pro-audio or HiFi fields, and so we are unlikely to see offerings from the pro-audio manufacturers for horns or waveguides specifically designed to address internal reflections, especially considering the requirement for mouth size expansion. This leaves the task to the DIY crowd, and a couple of examples from my workshop are shown in the lower half of fig 6, images: B & D. These are the same pair of axially symmetric Oblate spheroid waveguides which I described in the thread referenced earlier. The waveguide contours are compound, with the larger unit employing both a Tractrix mouth, and ¼ round radius at the mouth (this doubles the diameter). While the smaller unit utilizes a ½ round radius of smaller diameter, allowed by the use of a higher crossover frequency.

    The horizontal and vertical scales on all four graphs of fig 6 are identical, allowing direct comparison of ripple level between the four units. The DIY waveguides are seen to exhibit somewhat lower levels of ripple over the intended pass band compared to the commercial offerings. The ripple that is visible on the DIY spectra is longer period, which is consistent with the design of short axial dimension in these devices. The graphs are included not as a “shoot out” comparison, but simply to illustrate that a home hobbyist, armed with the knowledge of the mechanism which causes horn-honk, can build good sounding waveguides in their home workshop. Now, pick up a magazine, roll it up into a megaphone and talk through it, if you need further convincing that this is a worthy goal.

    Controlled Directivity in waveguides:
    On the “Erstaz.” thread, Rob posted a question addressed to me, on the subject of CD horns and diffraction:

    Quote Originally Posted by Robh3606
    Hello Jack, I have a question about both the Peavey horn and Earls…..snip…Rob


    The controlled directivity subject has a number of facets related to subjective sound quality of horns, which will require covering some background information in order to give a meaningful answer to the question.

    At the beginning of this thread, I listed the big four criteria for good sound reproduction, and I repeat the list here:
    1) Flat frequency response, both on axis and total radiated power.
    2) Wide frequency bandwidth. (20Hz -20kHz is sufficient)
    3) Wide dynamic range, meaning realistic peak output SPL, with low electrical and mechanical noise floor.
    4) Low distortion (all forms of non-linearity)

    Category #1), of the big four, lists the requirement for flat frequency response both on axis, and in terms of total radiated power. What that means is that an on-axis frequency response measured in an anechoic chamber should be flat, with no resonant peaks or troughs, no ripple, and no broad tilt or response variation (ruler flat is best). If the phase is well behaved, this will yield a good impulse response in the time domain.

    I additionally stated my criteria for flat response in terms of total radiated power, which relates to the requirement to generate both early reflections, and diffuse reverberant sound field with frequency response that mimics the direct arrival spectra. The spectra of the total radiated power could be measured in a “live” reverberation room at some distance from the speaker, independent of relative microphone-speaker angle.

    end of part 5 - Jack Bouska
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  6. #6
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    Factors Affecting Sonic Quality of Mid & HF Horns & Waveguides (Part #6 of 9)

    Why CD?
    My original interest in smooth power response was motivated by a series of articles which appeared over a number of years during the 1980’s, in an obscure Canadian magazine called Audio Scene Canada. The editor, Ian G. Masters, often reported on the research being conducted by Dr. F. Toole at the National Research Council (NRC) facilities in Ottawa. Dr Toole concluded that when frequency response, and other factors were held constant (and adequate), subjects in the extended blind listening tests reported strong preference for those speakers which exhibited the smoothest off axis response, and those that came closest to providing full omni directional response.

    Members of this forum will know of Dr Toole from his work with the Harman group of companies, and the strong influence that the NRC team has had on JBL home and pro-audio divisions. Dr Toole’s white papers on this and other subjects are mandatory reading
    http://www.harman.com/about_harman/technology_leadership.aspx (look under white papers).

    While I am not a fan of pure omni directional speakers (stereo image is too vague for my taste), I am a big proponent of using controlled directivity in the high frequency end of the spectrum to limit the adverse effect of early reflections, and improve the subjective tonality of the reverberant sound field in my listening room.

    For a reasonable synopsis of how this can be accomplished with CD waveguides, see the white paper written by Earl Geddes on the Summa loudspeaker and room placement:
    http://www.gedlee.com/downloads/Summa.pdf

    How to achieve CD:
    Under the assumption that CD is desirable for good room integration, the next question is: how do we simultaneously achieve both good CD, and good tone, in a driver & waveguide combination?

    Most waveguide designs require three features to achieve reasonable constant directivity performance:
    a) Conversion of plane waves into spherical waves via diffraction.
    b) Flare shape which guides the spherical waves without wave front distortion.
    c) Transducers which produce true plane waves over a broad range of frequencies.

    The full quote of Rob’s question is shown just below:
    Quote Originally Posted by Robh3606
    Hello Jack
    Quote Originally Posted by Robh3606
    I have a question about both the Peavey horn and Earls. In both cases the measurements stop at 10K. What actually going on above that frequency?? The 2344 used the diffraction slot width to determine the HF beam width limit in the horizontal plane. Both Earl’s horn and the Peavey don't have this feature so the smallest dimension is the throat diameter. In Earls I think it's a 1" throat while the Peavey is 1.6". Are the throat dimensions acting as a diffraction slot as far as the upper limit dispersion in concerned? Does the directivity change above 10K???
    Rob
    The peavey white paper that was referenced in the Ersatz thread can be found here:
    The Quadratic-Throat Waveguide (overview):
    http://www.installaa.com/downloads/pdf/qwp1.pdf#search=%22charlie%20hughes%20peavy%22
    and C. Hughes paper here:
    http://home.carolina.rr.com/charliehughes/Articles/QTWaveguide/QTWaveguide-Fr.html

    The first link gives a good historical review of CD horn design, and introduces the use of conical horns for defined coverage. The second link introduces the concept of: one parameter (1P) wave propagation, which turns out to be an important aspect of modern CD designs. 1P wave propagation is defined as an acoustic iso-pressure wave-front where the instantaneous pressure is a function of a single spatial coordinate.

    Only three types of 1P propagation exist for acoustic waves, namely: planar, cylindrical, and spherical waves.

    A planar wave travels along one of the three Cartesian coordinates, say X, while the instantaneous pressure is invariant over both the other coordinates, Y and Z. Think of a low frequency pressure pulse moving in a heating duct, or pipe, the pressure at the wave front is the same top to bottom, and side to side (width and height of the duct), and only varies by distance along the duct. The duct side walls act as perfect reflectors (acoustic mirrors), creating the same effect as if the wave was moving in open space.

    A cylindrical wave might be generated by a very, tall circular array of small ribbon transducers. In cylindrical coordinates, the low frequency components of the pressure pulse do not vary in the Z axis up and down the ribbon, or in the Theta angular axis, the pulse is invariant in circular arcs around the ribbons, so the pressure only varies with radius away from the center.

    A spherical wave, which might be generated from a very small omni directional transducer, has a low frequency pressure pulse that only varies by the radial distance from the center, so that pressure at a point in space is completely determined by the coordinates of time and radius.

    Perfect examples of 1P waves don’t really exist in the physical world, but if the frequency range is kept low enough, the approximations are close enough for wavelengths longer than any dimension of the transducer. For instance, PA line arrays are designed to emulate cylindrical wave generation.

    The motivation for discussing 1P waves is that compression driver phase plugs are designed to generate approximations to plane waves at their exit apertures. Modern CD waveguides work by launching sections of angle constrained spherical wave fronts. This trick requires a device that converts between 1P propagation types, by transforming plane waves into spherical waves. I know of three physical methods which can be used to change between plane waves and spherical propagation:

    1 – Reflection, such as the parabolic microphones used by birdwatchers and spies
    2 – Refraction, such as the acoustic lens discussed by Ausburger (http://www.lansingheritage.org/html/jbl/reference/technical/lens.htm )
    3 – Diffraction, as used by the majority of CD waveguides on the market

    Diffraction is in common use, because it really is the only practical method for converting the plane wave front from a compression driver exit, into a uniformly distributed sound field. There are other horn geometries, such as Tractrix, Acapella (or Avantgarde) "Kugelwellentrichter" shapes which are lumped into the category called “spherical horns”. Unfortunately, there is no magic flare rate, or horn shape which will convert plane waves into spherical waves. The “spherical” horn flares, or any other exponential, or hyperbolic, curve which has a large radius of curvature at the throat (slow expansion), followed by a smaller radius of curvature at the mouth (rapid horn diameter increase), will always exhibit increasing DI with increasing frequency. These horn types can only produce spherical wave fronts at the lowest frequencies, where the wavelength is equal or longer than the horn axial length. (Usually close to cutoff frequency). See discussion below for details.

    The majority of modern waveguides achieve broadband constant directivity by transforming the transducer generated plane wave to a spherical wave by passing the plane wave though some form of diffracting aperture, which expands into a (semi) conical horn flare. These CD waveguides need to have predominantly straight sided walls, which intersect with the edges, or center, of the diffraction aperture. The spherical wave front emitted by a diffraction aperture will always propagate perpendicular to straight sided (radial) walls. Any radical departure from straight sides will cause reflections and/or induce non-spherical (non-1P) expansion of the wave front, which will defeat the CD objective.

    end of part 6 - Jack Bouska

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