Rane AD22S "Environmental Effects on the Speed of Sound" Den - Page 2

problems. Perhaps an example best illustrates the importance of tightly controlling the environment of sound systems. 0.1 An Example For this example I will jump ahead and use data from the various graphs and tables presented. I hope this approach will encourage you to wade through the forthcoming material. As detailed as it must be, it is not terribly interesting. However, the results are. This simple example does not even require diagrams. Consider a listening spot located such that the direct sound must travel 50 ft (15 m) to the listener. This same spot receives one reflected arrival that travels 140 ft (42 m), say 70 ft (21 m) to a sidewall and another 70 ft (21 m) back to the listener's ear. Ignore all other delayed arrivals. The reflected wave arrives with some sort of phase relationship to the direct wave. This relationship is a function of the distance traveled, the frequency involved, and the speed of sound. Assume the room temperature was 20°C with 30% relative humidity when measurements where taken. Table 3 shows that the velocity of sound is 3.71% faster than standard velocity (1087.42 ft/s). Using a test tone of 10 kHz, calculate the following information: Velocity of sound 1087.42 x 1.0371 = 1127.763 ft/s Wavelength 1127.763 10 kHz = 0.1127763 ft Number of cycles 50 traveled for 50 ft 0.1127763 = 443.36 Number of cycles 140 traveled for 140 ft 0.1127763 = 1241.40 For purposes of this example, the only thing of interest is the decimal fractions of a cycle. For all practical purposes the two waves are in phase (0.36 cycle verses 0.40 cycle), that is, the delayed and attenuated reflected wave arrives essentially in phase. So the two waves will add. A little equalization easily corrects this bump and the sound contractor is happy. Until the environment changes. Assume the temperature rises to 30°C with 80% relative humidity. Consulting Table 3 shows that the velocity of sound now is 5.9% faster than standard. The casual observer mistakenly figures it is only a difference of 2.19%, so there is no problem. The casual observer is wrong. Recalculation gives the following: Velocity of sound Wavelength Number of cycles traveled for 50 ft Number of cycles traveled for 140 ft 1087.42 X 1.059 = 1151.578 ft/s 1151.578 = 0.1151578 ft 10 kHz 50 = 434.19 0.1151578 140 = 1215.72 0.1151578 Okay, the velocity of sound increased. This creates a longer wavelength. So traveling the same distances takes fewer cycles. Nothing too interesting yet. However, careful examination of the two decimal fractions of a cycle reveals that they are essentially out of phase. The difference between them is 0.53 cycle, or about 180°. Even to the casual observer this is not good. The applied equalization is now in the wrong direction. This example illustrates the fallacy of thinking that you can ignore velocity changes since they affect direct and reflected waves equally. This simply is not true. Complicating things further is the change in absorption due to the change in relative humidity. Table 6 and Fig. 6 show a drop of 39 dB per 1000 ft (300 m) due to the increased relative humidity (ignoring the temperature effects of 30°C). Since the example involves a distance of 140 ft, there is 5.46 dB less absorption. So not only does the signal arrive out of phase, but it is also about 5.5 dB bigger. The point of all this is that even a small percentage change in the speed of sound can have disastrous effects on a sound system. Often overlooked is that the small percentage change is for every cycle undergone by the wave. It is a trap to think of the change as only a few percent and dismiss it. Think of the hundreds and thousands of cycles existing within any sound room. Each one has its wavelength altered by this percentage. If a 1% change affects hundreds of cycles, it alters the acoustics of the whole system. No wonder that all those hours spent equalizing are sometimes in vain. 0.2 Overview Sec. 1 presents historical background information to put into perspective the number of years spent in investigating sound, its velocity, and the environmental factors affecting it. Temperature and humidity effects appear as Sec. 2. Following this, Sec. 3 outlines the effect of relative humidity on sound absorption, and finally, Sec. 4 gives a brief summary of the paper. Much work lies ahead in understanding how to control environmental effects so that room equalization, once done, will remain satisfactory for prolonged periods. I hope this paper succeeds in outlining the necessary areas of study and in stimulating others to probe further. 1 HISTORICAL BACKGROUND [1] Investigation into the nature of sound dates back to earliest recorded history. Indeed, ancient writings show that Aristotle (384-322 B.C.) observed two things regarding sound: first that the propagation of sound involved the motion of the air, and second that high notes travel faster than low notes. (Batting 0.500 is not too bad for the ancient leagues.) Since in the transmission of sound air does not appear to move, it is not surprising that other philosophers later denied Aristotle's view. Denials continued until 1660 when Robert Boyle in England definitely concluded that air is one medium for acoustic transmission The next question was, how fast does sound travel? As early as 1635, Pierre Gassendi, while in Paris, made measurements of the velocity of sound in air. His value J. Audio Eng. Soc., Vol. 36, No. 4, 1988 April