Question

A stationary police car sounds a siren with a frequency of $990Hz$. If the speed of sound is $330m/s$, an observer driving towards the car with a speed of 33 m/s, will hear a frequency of

• A. $891Hz$
• B. $900Hz$
• C. $1089Hz$
• D. $1100Hz$

Answer 1

Answer: (C)

$1089Hz$

From Dopplers effect, the perceived frequency $f_p$ is given by

$f_p$ = $f\left(\frac{v+v_o}{v}\right)$

Given, $f_p$ = 990 Hz, $v$ = 300m/s, $v_o$ = 33m/s

∴$f_p$ = $990\left(\frac{330+33}{330}\right)$ = $990$ $\times$ $\frac{363}{330}$ = $1089$ Hz