Waves are waves
Sep 1, 1999 12:00 PM, Glen Ballou
A study of the similarities and differences that exist between sound waves and light waves and some equations to quantify those defining characteristics.
We always compare. When we purchase a car, stereo, boat or camera, we look at how they differ and share common traits. In the field of audio and visual, it is interesting to compare optics to audio. This does not mean that we should design optical systems in the same way we design a sound reinforcement system, or vice versa; the comparison here is only used to help an audio person understand the optical system in terms familiar to audio and, conversely, an optical person understand an audio system in terms with which he is familiar.
In optics, we talk multi-screen, and in audio, we talk multi-channel. Multi-screen is two, three or more screens or screen areas, and it can be related directly to multi-channel, stereo or surround sound. In other words, the information being presented on each screen or by each loudspeaker is different, but it must, nevertheless, be related.
In designing a sound system, one of the first things we need to do is determine whether the loudspeaker will cover the audience area. One way to determine this is to lay out the loudspeaker coverage pattern on the plan and elevation view of the room to be covered as shown in Figure 1. This can be done manually or with one of the many programs available, such as EASE. Because the wavelengths of sound are long compared to the length of the loudspeakers producing the sound, sound does not necessarily travel in a straight line as it leaves the loudspeaker. Rather, it bends aroundobjects, including the loudspeaker, particularly at low frequencies. This causes varying Q and coverage angles of loudspeakers with frequency. Consequently, the analysis must include all the required frequencies of interest, usually between 125 Hz and 8 kHz. Most loudspeaker manufacturers supply coverage patterns for their loudspeakers. Some supply it at only one frequency and do not give the dB attenuati! on at the roll-off frequency. Th e more reputable manufacturers give the coverage at many frequencies and at the 3 dB, 6 dB and 9 dB levels.
In optics, the wavelength of light is much shorter than the lenses being used. Therefore, light appears to travel in a straight line, and the Q for lenses does not vary with the various colors we are transmitting. For long screen-to-film gate distances, Equation 1 (page 30) is used to determine image width. For short screen-to-film gate distances, such as are used in rear-projection systems in board rooms, the classical lens equation, Equation 2 (page 30), should be used.
In the case of 35 mm slides, image width to image height, or aspect ratio, is 1.5:1; 16 mm motion pictures have an aspect ratio of 1.33:1. Standard video has a ratio of 5:4, and HDTV has a ratio of 16:9. It is interesting that aspect ratios are given with respect to height, although most projection charts are related to width.
The equation for the geometric Q of a loudspeaker and lens is the same and can be found with the equation: where U is the horizontal coverage angle, and F is the vertical coverage angle.
The real Q of a loudspeaker, however, is less than the geometric Q because of diffraction, lobing and beaming, which varies with frequency. Optically, the real Q and the geometric Q are about the same, making optical Q measurements easier. Loudspeaker Q ranges from 1 to 50, while the optical Q can range from 14 to greater than 4,000, depending on the lens focal length.
To determine power required to produce the desired SPL in the audience area, loudspeaker sensitivity must be known. The loudspeaker sensitivity is given by the loudspeaker manufacturer and was determined by energizing it with 1 W of pink noise and measuring the sound pressure level with a sound level meter 4 ft (1 m) from the loudspeaker. The loudspeaker sensitivity is specified in sound pressure level in dB at 1 W/4 ft (1 W/1 m), Figure 2. If we need an SPL of 100 dB at 1 m, and the loudspeaker has a sensitivity of 100 dB/1 W/1 m, we need 1 W to produce the desired SPL. If the loudspeaker sensitivity was 97 dB/1 W/1 m, however, we would need 2 W to produce the desired SPL.
Optically, the sensitivity of a lens or the f/stop of a lens is the ratio of the focal length of the lens divided by the lens diameter. For instance, a 3 inch (76 mm) focal length lens with a 3 inch diameter would be rated as an f/1 lens. A 10 inch (254 mm) focal length lens with an f/1 rating would be 10 inches in diameter. As you can see, a sensitive long focal length lens would have to be extremely large to be sensitive. This is why long focal length lenses are seldom more sensitive than f/3.2. The actual light output differences would be the difference in area between the different f/stops; therefore, as the f/stops are halved or doubled, the sensitivity changes by a ratio of four. This is the same equation as used in photography. If you shoot a picture at 1/30 second at f/5.6, you would have to change the f/stop to f/4 if you change the speed to 1/60 second.
Efficiency is also an important parameter. A loudspeaker with a 1 W/4 ft sensitivity of 107.47 dB and a Q of 1 would have an efficiency of 100%. As the sensitivity of the loudspeaker decreases, so does the efficiency. Efficiency also decreases as the Q of the loudspeaker increases, which is the reason why low-frequency loudspeakers with low Q and low sensitivities are often more efficient than high-frequency horns with high Q and high sensitivities, as shown in Figure 3.
The efficiency of a lens is equal to the light output of the lens being tested divided by the light output of a perfect lens. The lens being tested will always be less than perfect because of the quality of the glass from which it is made, which creates some losses, and of reflections off the surfaces of the lens elements. Good lenses are coated to reduce this reflection. An uncoated lens may lose as much as 40% of the light output, while a good, coated lens may lose only 5%. For this, reason two different brands of f/2 lenses may not have the same efficiency; therefore, lenses used on a multiple screen should be matched for size and light output, as shown in Figure 3.
Once the loudspeaker to be used is determined, the amp power can be calculated by using the equation: where W subscript amplifier is the power required from the amp in watts to produce the desired SPL, program level is the desired program level in dB; Acoustic level change is the difference between the sound pressure level at the farthest listener and the reference distance in dB, and L subscript sens is the loudspeaker sensitivity at the reference distance in dB.
It is important that the amp power does not exceed the maximum power the loudspeaker is capable of accepting. If the amp power required is greater than the power capabilities of the loudspeaker, then either more loudspeakers or a more efficient loudspeaker must be used to accept the total amp power needed to deliver the required SPL. If the loudspeaker sensitivity is increased by 3 dB, the amp power can be reduced by 3 dB or cut in half. This is why it is important to use efficient loudspeakers when covering large areas with sound.
In the optical system, the projector output in lumen is equal to the luminance on the screen times the screen area divided by the screen efficiency and lens efficiency; where Lumens subscript projector is the lumens required at the projector to produce the desired brightness on the screen; Luminance required is the screen brightness required and is effected by room light and the subject projected (words require less brightness than pictures); Screen area is the area of the screen in square feet; % screen efficiency is the amount of light the screen reflects back to the audience (a matte white screen has an efficiency of 100%), and % lens efficiency is the efficiency of a lens relative to a perfect lens of 100%; this number is always less than 100%.
In a front-projection system, a matte white screen is considered 100% efficient or has a gain of one, while a beaded or high-gain screen or lenticular screen can have a gain of two to seven on axis. Being passive devices, screens cannot produce more than they receive, so when the screen is said to have gain, it is only on-axis and falls off to below one off axis. In rear projection, the on-axis screen gain can vary from 0.5 to 10. Unfortunately, high-gain rear-projection screens have a narrow viewing angle and, therefore, are only used when the audience is one or two people in a fixed position. For boardrooms, low-gain, wide-angle screens are used. Efficient lenses, like efficient loudspeakers, mean less power required. Because power is large, heavy and expensive, there is a decided cost and maintenance advantage in using high-efficiency and low power. If, on the other hand, the extra money is in the budget, and there is enough room to install the larger projector, the advanta! ge realized will be a brighter p icture. Normally, if a low-sensitivity lens is used, a sharper picture will result as it is easier to produce a lens with a large number f/stop (small diameter) than a lens with a small number f/stop (large diameter).
The final important matter to be determined acoustically is the articulation loss of consonants in rooms with reverberant times greater than 1.6 s and in its simple form is: where, RT60 is the reverberation time in 2 kHz octave band; D2 is the distance between the loudspeaker and the farthest listener; V is the volume of the room, and Q is the directivity of the loudspeaker.
If the loudspeaker Q is too low, the articulation loss will exceed 10%, or whatever criteria you decide, and the Q will have to be increased. The loudspeaker Q can be increased by either changing loudspeakers to ones with a narrower coverage pattern or by stacking loudspeakers. Increasing the Q of the loudspeaker may reduce the audience coverage area so that more loudspeakers are required, reducing articulation. If increasing Q is not possible, the distance D2 can be reduced, or the RT60 can be reduced. Reducing D2 requires moving the loudspeaker closer to the audience. This might reduce the audience coverage area to a point where more loudspeakers will be required to cover the area, again reducing articulation. Reducing RT60 almost certainly requires the help of an acoustician and a large budget.
If the ambient sound (noise) is too high, the S/N ratio (signal-to-noise) deteriorates to a point where the ambient noise must be reduced to improve intelligibility to an acceptance level. Reducing noise usually requires the service of an acoustician.
In projection systems, assuming the optics are of good quality (low distortion and minimal aberration), then acceptable viewing quality is basically determined by two parameters. First, like S/N ratio in sound, ambient light is the culprit in optics. The light that hits the screen and reflects back to the audience reduces intelligibility by reducing picture contrast. If ambient light hitting the screen is excessive, it must be reduced as increasing projector light output reaches a point of no return - a bright white output from a projector hitting a screen has very little contrast with a bright white light being produced by the sun or high intensity lights. One of the main advantages of rear projection is its ability to perform satisfactorily under relatively high ambient light. It is important, however, that the light be kept away from the screen as much as possible and imperative that the area behind the screen be as dark as possible.
The second parameter that produces a poor picture is a low Q lens (many wide angle lenses), which is a short focal length lens. Low Q requires the light waves to be bent excessively. This reduces sharpness in both front and rear projection. In front projection with high-gain screens, off-axis seating has greatly reduced brightness. Remember, passive devices cannot produce gain; so if you have gain head on, you will have reduced gain off-axis.
In rear-screen installations, a hot spot will appear in the center of the screen because this is the area where the light waves are bent the least. As the observers move to either side of the room, the hot spot moves with them and appears where the bend angle is the smallest, and the opposite side of the screen becomes dark. Increasing the focal length of the lens reduces the hot spot because the light waves are bent less at the screen. This usually increases the edge-to-edge screen brightness and improves picture quality. Unfortunately, it does require the projection room to be much deeper or a system of mirrors must be used. Sometimes high-quality optics must be traded off for space.
The third parameter effecting optics is the distance from the projector to the screen. Like a long D2 reduces the direct SPL by the square of the distance, long throw projection distances reduce the light output on the screen by the square of the distance. All things being equal, every time you increase the distance between the projector and the screen, you decrease the light on the screen. Although this can be overcome by improving the lens optics, the cost will rise considerably.
Nature has only a few rules we must follow. Fortunately for us, the rules in optics are very much the same as the rules in audio. If we become proficient in one, we can also become proficient in the other. All it takes is time and experience.
