.
The Doppler Shift. While driving a car, AJ honks the horn every 5 seconds. Hitch is
standing by the side of the road,
and hears the honks of the oncoming car every 4.6 seconds.
The speed of sound is 330 meters per second. Calculate the speed of AJ’s car.
Describe what Hitch hears after the car passes.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
car, t1 car, t2 Hitch
------------o---------------o-----------------------o--------------
---->
The figure shows the situation.
The car moves along the straight road from the left to the right towards Hitch.
At the time moment t = t1, when the distance from the car to Hitch is D1, the car releases the honk.
After 5 seconds, at the t = t2 = t1+5, when the distance from the car to Hitch is D2, the car releases the next honk.
The first honk arrives to the Hitch location at the time moment t = .
The next honk arrives to the Hitch location at the time moment t = .
The time difference between two successive honks arriving to Hitch location is
- = + = 5 + .
Also, D1 - D2 = 5*v, where v is the car speed.
So, you have this equation
5 - = 4.6, or = 0.4.
Hence, v = = 26.4 m/s.
Answer. The speed of the car is 26.4 m/s or 95.04 km/h.
Solved.