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I drive in my car at V_L=18 m/s down a road. The motorcycles are also driving do

ID: 1517605 • Letter: I

Question

I drive in my car at V_L=18 m/s down a road. The motorcycles are also driving down the road, both at 20 m/s. When one motorcycle is ahead of me, and one behind, I hear a beat frequency. The motorcycles' engines both produce a frequency of 400 Hz. The speed of sound is 344 m/s. What frequency do I hear from the motorcycle behind me? What frequency do I hear from the motorcycle ahead of me? What beat frequency do I hear? When a motorcycle is 3 m away, the intensity of the sound from the engine is 0.6 W/m^2. What is the sound intensity level (in decibels) of a single motorcycle engine at 3 m? If both motorcycles are 3 m away, what is the sound intensity level (in decibels) of the sound from both of their engines combined?

Explanation / Answer

a)     frequency from behind motorcycle =   [(344 - 18)/(344 - 20)] * 400

                                                               = 402.469 Hz

b)     frequency from ahead motorcycle =   [(344 + 18)/(344 + 20)] * 400

                                                               = 397.802 Hz

c)   Beat frequency =    f1 - f2

                                   =   402.469   -   397.802 = 4.667 Hz

d)    sound intensity level = 10 * log(0.6/10-12)

                                         = 117.78 dB

e)      sound intensity level for both motorcycles =   10 * log(1.2/10-12)

                                                                             = 120.79 dB