# Doppler effect speed of sound

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1. Oct 4, 2014

### calculator20

1. The problem statement, all variables and given/known data
Problem: a car is moving away from a stationary observer at 25ms^-1. It emits a frequency of 810Hz and the observer hears an apparent frequency of 762Hz. What is the speed of sound in air at that time?

2. Relevant equations
The equation for a source moving away is

f' = f(v/(v+us)) where us is speed of source.

3. The attempt at a solution
There are 2 v's and I need just one, I have no idea where to start, please can you help?

2. Oct 4, 2014

### Staff: Mentor

Of the two speeds, one is given. Just solve for the other.

3. Oct 4, 2014

### calculator20

Yes I know I have us but there are two v's in the equation and I don't know how to rearrange it to get one v on its own?

4. Oct 4, 2014

### Staff: Mentor

Ah, so it's the algebra that's messing you up. First thing to do is get rid of that denominator on the right hand side. How can you do that?

5. Oct 4, 2014

### calculator20

Multiply by it giving this?

f'v+fus = fv

6. Oct 4, 2014

### Staff: Mentor

Almost. That second term on the left should have an f', not an f.

7. Oct 4, 2014

### calculator20

Oh yes, sorry.

f'v + f'us = fv

I still can't see how I set it down to just one v without somehow cancelling both out along the way?

8. Oct 4, 2014

### Staff: Mentor

Keep the term with us where it is, but move all the others to the right. Then you can solve for us.

9. Oct 4, 2014

### calculator20

But I'm solving for v?

10. Oct 4, 2014

### Staff: Mentor

No, v is the speed of the car. You need to solve for us, which is the speed of sound.

11. Oct 4, 2014

### calculator20

It's definitely v I need to find. According to my text book us is the moving source velocity. In the other equation it uses uo as moving observer velocity.

12. Oct 4, 2014

### Staff: Mentor

You're right! (I must be losing my mind. Sorry about that!)

So just collect all the terms with v in them to one side. Then you can isolate v. [Using ax + bx = (a+b)x]

13. Oct 4, 2014

### calculator20

f'us=fv-f'v

f'us =v(f-f')

v=f'us/(f-f')

Is that right?

14. Oct 4, 2014

### Staff: Mentor

Perfect!

15. Oct 4, 2014

### calculator20

Excellent! Thank you so much for your help! :)