Calculating the Frequency of a Car Horn Using the Doppler Effect

[Morgan89]

Two automobiles are equipped with the same single-frequency horn. When one is at rest and the other is moving toward an observer at 13 m/s, a beat frequency of 5.8 Hz is heard. What is the frequency the horns emit? Assume T = 20°C.

I understand that this is related somehow to the doplar effect. I thought to use the equation to find the heard velocity when a sound is moving towards a listener which is...
Frequency Heard = Frequency Sound (Velocity of Sound/(Velocity of sound- velocity of moving sound)

This formula should work, but i am wondering if i can assume beat frequency is the actual frequency of the sound. I feel as though it is not. I need to know how to use this beat frequency to find the actual frequency of the sound. HELP!

 

[Archduke]

How is the beat frequency related to the difference of the frequencies (caused by the doppler shift) of the horns? This will allow you to find the difference in frequency caused by the Doppler shift and therefore the frequency the horns emit.

 

[Morgan89]

So if i say the frequency heard of the moving car is F of sound * (v/v-velocity of moving car) then i can just say that the difference between that value and the regular f of sound equals the 5.8 beat frequency right?

 

[Archduke]

Yep, that's right:

$$f_{beat}=|f_{2}-f_{1}|$$

And you know $$f_{2}$$ in terms of $$f_{1}$$ from the doppler shift equation; so put it all together, and you should get the right answer!

 

[Morgan89]

I got It! 100 on my Final! Whooo Hooo! I love you all!

 

[Archduke]

I got It! 100 on my Final! Whooo Hooo! I love you all!

Congrats, and well done!