Question

The siren on an ambulance is emitting a sound whose frequency is 2550 Hz. The speed of sound is 343 m/s. (a) If the ambulance is stationary and you (the "observer") are sitting in a parked car, what are the wavelength and the frequency of the sound you hear? (b) Suppose that the ambulance is moving toward you at a speed of 26.2 m/s. Determine the wavelength and the frequency of the sound you hear. (c) If the ambulance is moving toward you at a speed of 26.2 m/s and you are moving toward it at a speed of 16.0 m/s, find the wavelength and frequency of the sound you hear.

Answer #1

a)

Wavelength , = c/f = 343/2550 = 0.135 m

Frequency , f = 2550 Hz

b)

f' = f*c/(v + c)

Here, f' = apparent frequency heard.

f = original frequency

c = speed of sound = 343 m/s

v = speed of the source.

So, f' = 2550*343/(343 - 26.2) = 2761 Hz <------ answer

apparent wavelength, ' = c/f' = 343/2761 = 0.124 m <---- answer

c)

f' = f*(c + v1)/(c - v2)

v1 = 16 m/s

v2 = 26.2 m/s

So, f' = 2550*(343 + 16)/(343 - 26.2 )

= 2890 Hz <------ answer

So, ' = 343/2890 = 0.119 m <------ answer

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