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

Step-by-step 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((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[(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`