Question

A police car horn emits a frequency 250Hz when it is at rest. What frequency does a stationary observer hear if the police car sounds its horn while approaching at a speed of $27m{s}^{-1}$ ? What frequency is heard if the horn sounded as the car is leaving at $27m{s}^{-1}$ ? Velocity of sound $=340m{s}^{-1}$?

• A. 271 Hz, 231 Hz
• B. 271 Hz, 252 Hz
• C. 271 Hz, 225 Hz
• D. 271 Hz, 261 Hz

Answer 1

The correct option is A 271 Hz, 231 Hz

$f=250H_Z$
$v_s=27m{s}^{-1}$
$v=340m{s}^{-1}$
f’ = ?
When the car approaches the observer
$f^{\prime }=\frac{fv}{v-v_s}=\frac{250\times 340}{340-27}=271.6Hz$
When the car moves away from the observer
$f^{\prime }=\frac{fv}{v+v_s}=\frac{250\times 340}{(340+27)}=231.6Hz$