Question

A truck horn emits a sound with a frequency of 238 Hz. The truck is moving on a straight road with a constant speed. If a person standing on the side of the road hears the horn at a frequency of 220 Hz, then what is the speed of the truck? Use 340 m/s for the speed of the sound.

Answer 1

`v_s=27.8m/s`

Step-by-step explanation:

If the person hearing the sound is at rest, then the equation for the frequency heard
`f` given the emitted frequency
`f_0`, the speed of the truck
`v_s` and the speed of sound
`c` will be:

`f=f_0(c)/(c+v_s)`

Where
`v_s` will be positive if the truck is moving away from the person, and negative otherwise. We then do:

`(f)/(f_0)=(c)/(c+v_s)`

`(f_0)/(f)=(c+v_s)/(c)=1+(v_s)/(c)`

`v_s=c((f_0)/(f)-1)=(340m/s)((238Hz)/(220Hz)-1)=27.8m/s`