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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

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Answer:

37.42 m/s

Explanation:

We know that apparent frequency, [tex]\bar f[/tex] is given by

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

[tex]440=392\times \frac {343}{343-V_s}\\343-V_s=392\times \frac {343}{440}=305.5818182\\V_s=343-305.5818182=37.41818182\approx 37.42 m/s[/tex]

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