Question

Two automobiles are equipped with the same singlefrequency horn. When one is at rest and the other is moving toward the first at 20 m/s , the driver at rest hears a beat frequency of 9.0 Hz.

Requried:
What is the frequency the horns emit?

Answer 1

Answer: f ≈ 8.5Hz

Explanation: The phenomenon known as Doppler Shift is characterized as a change in frequency when one observer is stationary and the source emitting the frequency is moving or when both observer and source are moving.

For a source moving and a stationary observer, to determine the frequency:

`f_(0) = f_(s).(c)/(c-v_(s))`

where:

`f_(0)` is frequency of observer;

`f_(s)` is frequency of source;

c is the constant speed of sound c = 340m/s;

`v_(s)` is velocity of source;

Rearraging for frequency of source:

`f_(0) = f_(s).(c)/(c-v_(s))`

`f_(s) = f_(0).(c-v_(s))/(c)`

Replacing and calculating:

`f_(s) = 9.((340-20)/(340))`

`f_(s) = 9.(0.9412)`

`f_(s) =` 8.5

Frequency the horns emit is 8.5Hz.