Tech Talk
The Answer Man: Live Sound's tech guru answers some email quastions from our readers

Question:
A while ago, I wondered what caused a Constant Directivity (CD) horn to exhibit a roll-off different from any other. I made the assumption the phenomenon existed after seeing numerous processing products that include "CD horn compensation."

I was told that no such thing existed, and that the roll-off exhibited was due to the break point associated with the diaphragm mass of the driver.

Could you please elaborate on what the truth is here? And what is this break point due to diaphragm mass? Does this exist?

Answer:
CD horns slot-load the driver at the horizontal break point of the horn. You can see it, if you look at the front of the horn into the bell. For most all CD horns, this will be a vertical slot where the two sides of the horn bell meet. This slot creates a diffractional effect that causes all the driver's energy to radiate evenly between the horn walls, thus creating "constant directivity" from the lowest frequency. The horn loads the driver in the horizontal plane up to the frequency where the slot is wider than the wavelength.

This low-frequency loading point is evident in the vertical beam-width plot of the horn's specifications. However, a driver's total acoustic power output declines with increasing frequency, therefore the overall output level must decline as the frequency increases above the mid-band range where the driver is most efficient. CD horn EQ boost is employed to counteract this phenomenon, producing a flatter response to the upper limit of the driver's response.

Radial horns narrow in beam-width as frequency increases. Thus the lesser energy of the driver at higher frequencies still produces a flatter response on axis and needs no boost EQ. CD horns were invented to counteract this narrowing of beam-width at high frequencies that the then-common radial horn exhibited. In order to maintain the flat on-axis response that everyone was used to, HF EQ boost was necessary.

The Diaphragm Break-Point phenomenon is more commonly known as the first break-up mode. The first break-up mode occurs when the wavelengths through the material of the diaphragm, not through air, become smaller than the diameter of the diaphragm. This is not a roll-off of frequency response, but a deep notch in the higher frequencies usually followed by resonant peaks and more notches even higher in frequency. This notch can be 20dB deep, if your measurement system's sample points are at the right frequencies.

A typical aluminum four-inch diaphragm will have this notch at a lower frequency than an aluminum three-inch diaphragm. Likewise, a titanium or beryllium diaphragm will have a higher first break-up mode than a similar diameter aluminum diaphragm. This is because the speed of sound through those materials is faster than it is through aluminum. Paper cone speakers also have the same characteristics occurring at much lower frequencies. Break-up modes and resonances of 15-inch drivers show up, if the LPF of the crossover is removed.

Question:
I have been told that line arrays have a cylindrical wave front and their level attenuates at only 3dB per doubling of distance. Is this true?

Answer:
First, let's discuss the cylindrical wave front idea. This is an idealized explanation for what happens with a straight line array, and does not accurately describe the more common curved-J arrays seen in concert pictures and advertisements.

If you ignore the small side lobes at the top and bottom of the array, which are an artifact of the individual speaker spacing and vertical coverage overlap, the coverage of a straight line array looks similar to one-quarter of a single layer of a round cake or can of tuna. Geometrically, this approximates a cylindrical segment. The dispersion of a perfect point source is a spherical wave front. The cylindrical wave front dispersion pattern of a line array is not perfect, but is close enough to draw a comparison and is easy to visualize. In fact, the vertical dispersion does vary with frequency and undulates with distance within this near-field effect. Undulates means that the level goes up and down, like an oscillation as the distance increases, though the overall level follows a -3dB slope as distance increases.

Now let's look at the 3dB loss per doubling of distance. This effect is only true in the near field, where the height of the array is multiples of the wavelength. The near field is the distance range where the level attenuates at roughly 3dB per doubling of distance. Where this effect no longer occurs, called the far field, is where the line array begins to look like a point source and the level drops at 6dB per doubling of distance like any radiant energy point source. Derived by Mark Ureda for JBL, the formula for the division between the near field and far field, known as the critical distance, is:

Critical distance = (array length2 x frequency)/2300

This formula is in feet. Also, note that frequency is a part of the equation and that the higher the frequency, the greater the critical distance. For example, for an array 30 feet tall, 100Hz will have a near field that only extends 39 feet. However, the near field for 10,000Hz extends to 3,913 feet! This means that there will be a lot more high frequency content than low at greater distances, which is somewhat compensated for by air attenuation. This also means that for very long wavelengths (very low frequencies), there is no near-field condition for an audience even a few feet away from the array.

Curved-J arrays exhibit this effect perfectly, where there is no splay between boxes, usually at the top of the array. Where the curve is greater at the bottom of the array, this effect is much weaker.

Now how are you going to tune this puppy by ear?

John Murray is a 26-year industry veteran working for EV, Midas, MediaMatrix and TOA. John has presented two AES papers, chaired three Syn-Aud-Con workshops, and is a member of the TEF Advisory Committee and ICIA adjunct faculty.

If you have a question you would like to ask Live Sound!'s Technical Editor, e-mail him at jmurray@livesoundint.com

September/October 2002 Live Sound International