Solving for Speed of a Moving Car with Sound Frequency

[Jbreezy]

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.

 

[TSny]

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.

 

[Jbreezy]

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]

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.

 

[Jbreezy]

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]

That looks correct. Good work!