- #1

Potatochip911

- 318

- 3

## Homework Statement

You are moving at a speed of 35m/s and hear a siren coming from behind you and observe the frequency to be 1370 Hz. The siren goes past you and the new frequency heard is 1330 Hz. What is the speed of the siren traveling at? The speed of sound in air is 340m/s.

f

_{1}=1370 Hz

f

_{2}= 1330 Hz

D=35m/s

V=340m/s

## Homework Equations

f

^{l}=f

_{o}*((V+D)/(V+S))

## The Attempt at a Solution

Since the original frequency is not given I decided to make 2 equations with the different frequencies then just divide to eliminate the original frequency.

f

_{1}=f

_{o}*((V+D)/(V-S)) <-Since the siren is approaching

f

_{1}*(V-S)=f

_{o}*(V+D)

f

_{2}=f

_{o}*((V-D)/(V+S)) <-Since the siren is moving away

f

_{2}*(V+S)=f

_{o}*(V-D)

Dividing the 2nd equation by the first,

[f

_{2}*(V+S)]/[f

_{1}*(V-S)]=(V-D)/(V+D)

Letting C=f

_{2}/f

_{1}

C(V+S)(V+D)=(V-D)(V-S)

C(V

^{2}+SV+DV+SD)=(V

^{2}-DV-SV+SD)

CV

^{2}+CSV+CDV+CSD=V

^{2}-DV-SV+SD

CV

^{2}+CDV+DV-V

^{2}=-SV+SD-CSD-CSV

CV(V+D)+V(D-V)=S(-V+D-CD-CV)

S={V[C(V+D)+(D-V)]/[V(-1-C)+D(1-C)]}

Which gives me S=-40m/s which doesn't make any sense, I'm not sure where my mistake is but the correct answer is +40m/s.