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

Question

I drive in my car at V_L = 18 m/s down a road. Two 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

Frequency shift due to Doppler effect is given by,
f/ = f (v +/- vO) / (v -/+ vs )
vo = 18.0 m/s
v = 344 m/s
vs = 20.0 m/s
f = 400 Hz

(a)
f/ = 400*(344 - 18.0) / (344 - 20)
f' = 402.47 Hz

(b)
f/ = 400*(344 + 18.0) / (344 + 20)
f' = 397.8 Hz

(c)
Beat freq, = 402.47 - 397.8 Hz = 4.67 Hz

(d)
I(dB) = 10 * log(I/Io)
I(dB) = 10 * log(0.6/10^-12)
I(dB) = 117.78 dB

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