Question

At what speed a car is approaching a stationary observer if he hears the sound of a car siren with the frequency of 10% higher than the actual frequency.The speed of sound is 340 m/s . please answer this question with solution

Answer 1

Answer:

The car is approaching the observer at 30.90 m/s

Explanation:

This is the question of Doppler's Effect

Let the speed of the car is $v_S$

if the actual frequency is f then the listener hears it at

$f_L=f+f\times\frac{1}{10}$

$f_L=\frac{11f}{10}$

frequency heard by listener is given by

$\boxed{f_L=\frac{v+v_L}{v-v_S} f}$

Here, velocity of listener $v_L=0$

velocity of sound $v=340$ m/s

Therefore,

$\frac{11f}{10}=\frac{340+0}{340-v_S} f$

$\implies \frac{11}{10}=\frac{340}{340-v_S}$

$\implies \frac{340-v_S}{340}=\frac{10}{11}$

$\implies 340-v_S=\frac{10}{11}\times 340$

$\implies 340-v_S=309.09$

$\implies v_S=340-309.09$

$\implies v_S=30.90$ m/s

Therefore, the car is approaching the observer at 30.90 m/s