Question

A car speeding down the highway honks its horn, which has a frequency 392 Hz, but a resting bystander hears the frequency 440 Hz. If the speed of sound in air is 343 m/s, how fast is the car moving

Answer 1

37.42 m/s

Step-by-step explanation:

We know that apparent frequency,
`\bar f` is given by

`\bar f=f\frac {V}{V-V_s}` where f is the given frequency in this case 392, V is the speed of sound in air which is given as 343 and
`V_s` is the speed of car which is unknown, \bar f is given as 440 Hz

`440=392* \frac {343}{343-V_s}\\343-V_s=392* \frac {343}{440}=305.5818182\\V_s=343-305.5818182=37.41818182\approx 37.42 m/s`