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:

$f_{0} = f_{s}.\frac{c}{c-v_{s}}$

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:

$f_{0} = f_{s}.\frac{c}{c-v_{s}}$

$f_{s} = f_{0}.\frac{c-v_{s}}{c}$

Replacing and calculating:

$f_{s} = 9.(\frac{340-20}{340})$

$f_{s} = 9.(0.9412)$

$f_{s} =$ 8.5

Frequency the horns emit is 8.5Hz.