Question

A police car's siren operates at a frequency of 2,000 Hz. What frequency would a stationary listener observe if the police car is driving towards him at 65 mph? Note vsound = fλ, where vsound (the speed of sound in air) is 345 m/s. Also, 1 mile = 1.609 km.

Answer 1

we can use formula

$f_L=f_s(\frac{v_a-v_p}{v_a+v_p} )$

where

fL is listener frequency

fs is siren frequency

va is the speed of sound in air

vs is police car speed

so, we have

$f_s=2000Hz$

$v_a=345m/s$

$v_p=65mph$

now, we can change it into m/s

$v_p=65*\frac{1609}{3600}m/s$

$v_p=29.05139m/s$

now, we can plug it

$f_L=2000(\frac{345-29.05139}{345+29.05139} )$

$f_L=1689.33263Hz$..............Answer