A bird is flying directly toward a stationary bird-watcher...

A bird is flying directly toward a stationary bird-watcher and emits a frequency of $1250 \mathrm{~Hz}$. The bird-watcher, however, hears a frequency of $1290 \mathrm{~Hz}$. What is the speed of the bird, expressed as a percentage of the speed of sound?

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Key Concepts

Speed of Sound

The speed of sound is the rate at which sound waves travel through a medium and serves as a fundamental reference point in acoustics. When an object's speed is compared to the speed of sound—often expressed as a percentage—it provides insight into the dynamics of sound propagation and the resulting frequency changes observed.

Relative Motion in Wave Propagation

Relative motion in wave propagation refers to how the movement of the source or observer, in relation to the medium in which the wave travels, affects the observed wave properties. This principle is key to applying the Doppler Effect formula for calculating speeds.

Doppler Effect

The Doppler Effect describes the change in frequency or wavelength of a wave in relation to an observer when there is relative motion between the source and the observer. It is used to explain why the frequency of a sound increases when the source approaches the observer and decreases when it moves away.

Frequency Shift

Frequency shift is the phenomenon where the observed frequency of a wave differs from the emitted frequency due to the relative motion between the source and the observer. In this context, the increase in the observed frequency indicates that the source (the bird) is moving toward the observer.

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