Sound Waves Sound is a result of waves applying pressure to a persons eardrum. For a

Chapter 5, Problem 76

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Sound Waves Sound is a result of waves applying pressure to a persons eardrum. For a pure sound wave radiating outward in a spherical shape, the trigonometric function P = a r cos a 2pr l - ctb can be used to model the sound pressure at a radius of r feet from the source, where t is time in seconds, l is length of the sound wave in feet, c is speed of sound in feet per second, and a is maximum sound pressure at the source measured in pounds per square foot. (Source: Beranek, L., Noise and Vibration Control, Institute of Noise Control Engineering, Washington, D.C.) Let l = 4.9 ft and c = 1026 ft per sec. (a) Let a = 0.4 lb per ft2. Graph the sound pressure at distance r = 10 ft from its source in the window 30, 0.054 by 3-0.05, 0.054. Describe P at this distance. (b) Now let a = 3 and t = 10. Graph the sound pressure in the window 30, 204 by 3-2, 24. What happens to pressure P as radius r increases? (c) Suppose a person stands at a radius r so that r = nl, where n is a positive integer. Use the difference identity for cosine to simplify P in this situation.