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((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*(1609)/(3600)m/s`

`v_p=29.05139m/s`

now, we can plug it

`f_L=2000((345-29.05139)/(345+29.05139) )`

`f_L=1689.33263Hz`..............Answer