Question

you are driving at 22 m/s away from a police cruiser that is chasing you at 60 m/s. you hear the siren as 412 Hz,

What is the frequency, in units of hertz of the siren produced by the police cruiser? (Assume V=340 m/s )

Answer 1

Solution:

Velocity of the observer (you) (v​​​​​​o​​​)= 22 m/s

Velocity of the source (police cruiser)(v​​​​​​s​​​)=60m/s

Velocity of sound (v) = 340 m/s

Observed frequency (f')= 412 Hz

Since observer is moving away from the source and the source is approaching towards observer, according to Doppler's formula,

f'= f×[(v-v​​​​o​​​)/(v-v​​​​s​​​)].

Where,f = frequency of source(siren)

Or, 412= f×[(340-22)/(340-60)]

Or, 412= f× [318/280]

Or, f= 280× 412/318= 362.77 Hz

So the frequency of the siren produced by police cruiser is 362.77 Hz