# Doppler effect

## Homework Statement

A race car is traveling towards you and you hear a sound a frequency 3895.9 Hz. Then the car shoots by you. As the car moves away you hear a frequency of 2574.6 Hz. What is the speed of the car? Assume the temperature of the air is 20 degrees Celsius.

## Homework Equations

F_o = frequency of observer. Fs = frequency of source.

A source moving towards a stationary observer.
F_o = Fs1( 1 / (1-vs/v)

A source moving away from a stationary observer.

F_o = Fs2( 1 / (1+vs/v)

## The Attempt at a Solution

So I thought that I could set the two equal and solve for vs but this is not a good plan because It doesn't simplify nice. At least my attempts didn't.

Fs1( 1 / (1-vs/v) = Fs2( 1 / (1+vs/v)
I'm actually confused on this because I thought the question was giving me the frequency the observer hears which is F_o ??
I'm lost please point me in right direction.

## Answers and Replies

TSny
Homework Helper
Gold Member
F_o = frequency of observer. Fs = frequency of source.

A source moving towards a stationary observer.
F_o = Fs1( 1 / (1-vs/v)

A source moving away from a stationary observer.

F_o = Fs2( 1 / (1+vs/v)

I'm actually confused on this because I thought the question was giving me the frequency the observer hears which is F_o ??

Yes, you are given the frequencies heard by the observer. You might want to call these frequencies F01 and F02. How does Fs1 compare to Fs2?

Think about the ratio of the two equations.

Could I set sf1 = sf2 ...Man I'm not sure. I think it would be the same right? Because the frequency of the source is constant it doesn't change right?

TSny
Homework Helper
Gold Member
Could I set sf1 = sf2 ...Man I'm not sure. I think it would be the same right? Because the frequency of the source is constant it doesn't change right?

That's right. The source frequency is fixed.

F_o1 = Fs1( 1 / (1-vs/v)

F_o2 = Fs1( 1 / (1+vs/v)

I did

F_o1/F_o2 = (Fs1( 1 / (1-vs/v))/ (Fs1( 1 / (1+vs/v))
Fs1 and Fs2 cancel because the source puts out the same frequency.

I simplified this to get vs. I got something of the form..

vs = (v(fo1 - fo2))/ (fo2 + fo1)
I put in the numbers. v was determined to be v = (331+ 0.6(20°C))m/s
v = 343m/s put this in for v

vs = ((343)( 3895.9 - 2574.6)) / (3895.9 + 2574.6)
vs= 70.04 m/s

Please check my answer and see if I did it correct the answer seems reasonable to me. Thanks

TSny
Homework Helper
Gold Member
That looks correct. Good work!