A listener at rest (with respect to the air and the ground)...

A listener at rest (with respect to the air and the ground) hears a signal of frequency $f_{1}$ from a source moving toward him with a velocity of 15 $\mathrm{m} / \mathrm{s}$ , due east. If the listener then moves toward the approaching source with a velocity of 25 $\mathrm{m} / \mathrm{s}$ , due west, he hears a frequency $f_{2}$ that differs from $f_{1}$ by 37 Hz. What is the frequency of the source? (Take the speed of sound in air to be 340 $\mathrm{m} / \mathrm{s}$ .)

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Key Concepts

Speed of Sound

The speed of sound is the rate at which sound waves travel through a given medium, and it is a critical parameter in applying the Doppler effect formula in acoustics. Since the observed frequency shift depends on the ratio of the relative speeds to the speed of sound, knowing this value is essential for accurate calculations.

Frequency Shift

A frequency shift is the difference between the observed frequency and the actual emitted frequency from a source. In problems involving the Doppler effect, the magnitude of the shift can be used to infer either the speed of the moving source or the emitted frequency, depending on the known parameters.

Relative Motion

Relative motion in the context of wave propagation describes how the speed of the observer and the source with respect to the medium (in this case, air) affects the frequency that is perceived. The velocities of both the source and the observer must be taken into account to determine the resultant frequency shift.

Doppler Effect

The Doppler Effect refers to the change in frequency (or wavelength) of a wave as observed by someone who is moving relative to the source of the wave. This principle explains how the observed frequency increases when the source and observer are moving closer and decreases when they are moving apart.

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