Question

A fire engine's siren is 1400 Hz when at rest. Assume that the speed of sound is 343 m/s in air.

What frequency do you detect if you move with a speed of 21 m/s toward the fire engine? (Express your answer to two significant figures.)

What frequency do you detect if you move with a speed of 21 m/s away from the fire engine? (Express your answer to two significant figures.)

Answer 1

Actual frequency of sirun = n =1400 Hz
apparent freq

n' = n [v - vo] / [v - vs]
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in this combined formula, all v, vo, vs are moving in one direction (say +x). if 1 is in opposite direction, then it has to be resoved in +x.
v = speed of sound =343 m/s
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a) let source (engine) at origin. vs =0 given
vo = - 30 m/s
(observer going to source, -ve x, so made in +x direction)
v = + 343 m/s
sound speed moving in + x (reaching observer)

n ' = 1400[343 - (-21)] / [343- 0]
n ' = 1400*[1.061] = 1485.71 Hz
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b) away from engine
v=+343 , vo = + 21, vs =0
n ' = 1400[343 - 21] / [343 - 0]
n ' = 1400*[0.938] = 1314.28 Hz