Question

The siren of a police car is heard by a sitting at a cafe. The police car is traveling at 1.10 x 105 km/hr. If the siren has a frequency of 1.02 kHz, calculate the frequency heard by the person as the car moves towards and then away from them.

Answer 1

(A) When the frequency heard by the person as car moves towards him

As we the doppler formula

f(L) = (c + v (L)) / ( c - v(S)) * f(S) ...........................(1)   

Where f(L) = listener frequency, f(S) = source frequency , v(L) = listiner velocity . v(S) source velocity and c = speed of light (343 m/s)

Here person is at rest so

v(L) = 0 m/s

v(S) = 1.10 * 105 = 115.5 Km/hr

f(S) = 1.02 kHz or 1020 Hz

f(L) = ?

Putting these values in equation (1)

f(L) = ( 343 + 0)/(343-115.5) * 1020

f(L) = 1537.8 Hz or 1.537 kHz

(B) Now the frequency of siren when car move away from him

Now the formula is

f(L) = (c + v (L)) / ( c + v(S)) * f(S)

f(L) =  ( 343 + 0)/(343 + 115.5) * 1020

f(L) = 763 Hz or 0763 kHz