Question

You are driving along a highway at 35.0 m/s when you hear the siren of a police car approaching you from behind and you perceive the frequency as 1310 Hz. You are relieved that he is in pursuit of a different speeder when he continues past you, but now you perceive the frequency as 1240 Hz. What is the frequency of the siren in the police car? The speed of sound in air is 343 m/s.

Answer 1

Answer:

$f_{police}=1268.7 Hz$    

Explanation:

We can use Doppler equation to find the frequency of the siren.

First of all we have the police car moving behind the car. Hence, the frequency detected by the car will be:  

$f_{car1}=f_{police}(\frac{v_{s}-v_{car}}{v_{s}-v_{police}})$      (1)

Now, when the police car is moving in front of the car, the frequency detected by the car will be:

$f_{car2}=f_{police}(\frac{v_{s}+v_{car}}{v_{s}+v_{police}})$        (2)            

By solving equation (1) and equation (2) for $v_{police}$ we have:

$v_{police} = 44.67 m/s$

Knowing that:

• f(car1) = 1310 Hz
• f(car2) = 1240 Hz
• Vs = 343 m/s
• V(car) = 35 m/s

Finally, we just need to put this value into the first equation to find frequency of the police car.

$f_{police}=f_{car}(\frac{v_{s}-v_{police}}{v_{s}-v_{car}})$    

$f_{police}=1310(\frac{343-44.7}{343-35})$  

$f_{police}=1268.7 Hz$    

I hope it helps you!