Question

A stationary horn emits a sound with a frequency of 228 Hz. A car is moving toward the horn on a straight road with constant speed. If the driver of the car hears the horn at a frequency of 246 Hz, then what is the speed of the car? Use 340 m/s for the speed of the sound

Answer 1

Answer: 26.84 m/s

Explanation:

Given

Original frequency of the horn $f_o=228\ Hz$

Apparent frequency $f'=246\ Hz$

Speed of sound is $V=340\ m/s$

Doppler frequency is

$\Rightarrow f'=f_o\left(\dfrac{v+v_o}{v-v_s}\right)$

Where,

$v_o=\text{Velocity of the observer}\\v_s=\text{Velocity of the source}$

Insert values

$\Rightarrow 246=228\left[\dfrac{340+v_o}{340-0}\right]\\\\\Rightarrow 366.84=340+v_o\\\Rightarrow v_o=26.8\ m/s$

Thus, the speed of the car is $26.84\ m/s$