Question

Two cars have identical horns, each emitting a frequency of fs = 406 Hz. One of the cars is moving with a speed of 10.5 m/s toward a bystander waiting at a corner, and the other car is parked. The speed of sound is 343 m/s. What is the beat frequency heard by the bystander?

Answer 1

Answer:

$f_{B}=12.8 Hz$

Explanation:

Let's start finding the frequency heard by the bystander due to the moving car. We need to use Doppler effect here:

$f_{obs}=f_{s}\left(\frac{v}{v-v_{car}}\right)$    

v is the speed of sound (v = 343 m/s)  

So, we have:

$f_{obs}=406\left(\frac{343}{343-10.5}\right)=418.8 Hz$                  

Now, the beat frequency heard by the bystander is the combine of the frequencies, it means the difference between them. Therefore the equation is given by:

$f_{B}=f_{obs}-f_{s}=418.8-406=12.8 Hz$    

I hope it helps you!