# Physics wave question

## Homework Statement

a cyclist and a car are approaching each other at the same speed. the car makes a 500 Hz sound at 343 m/s. the cyclist hears the sound as 535 Hz. How fast are they moving?

## Homework Equations

f2 = f1(v/v$$\pm$$vs)

## The Attempt at a Solution

535 hz = 500 hz(343 m/s$$\div$$343 m/s-vs)
vs = 22.4 m/s

but the answer should be 11 m/s
HELP ??

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In this case, both the source and the receiver move, so u must use the general Dopple formula, not the specific formula for each case the source moves or the receiver moves.

f' = f.(V+Vr)/(V-Vs)

f: frequency created.

V: speed of the wave (sound or light).

Vr: velocity of the receiver: positive if moving toward the source, otherwise it's negative.

Vs: velocity of the source: positive if moving toward the receiver, otherwise it's negative.

In this case, Vs=Vr, and they're both positive. U will get the result 11,6 m/s. Be happy :D

great thanks!