How does the Doppler effect explain the change in sound frequency?

The Doppler effect explains the change in sound frequency as a result of the relative motion between a sound source and an observer. Here’s how it works:

Principle

The Doppler effect describes how sound waves are compressed or stretched depending on the movement of the source or the observer:

• Compressed Waves: When the source and observer are moving closer together, the sound waves get compressed, increasing the frequency (higher pitch).
• Stretched Waves: When the source and observer are moving apart, the sound waves stretch out, decreasing the frequency (lower pitch).

Key Scenarios

1. Source Moving Toward Observer:
   • The wavelength of the sound decreases.
   • Frequency increases, resulting in a higher-pitched sound.
   • Example: An ambulance siren sounds higher-pitched as it approaches.
2. Source Moving Away from Observer:
   • The wavelength of the sound increases.
   • Frequency decreases, resulting in a lower-pitched sound.
   • Example: The same ambulance siren sounds lower-pitched as it moves away.
3. Stationary Source and Moving Observer:
   • If the observer moves toward the stationary source, they encounter sound waves more frequently, increasing the perceived frequency.
   • If the observer moves away, they encounter sound waves less frequently, decreasing the perceived frequency.
4. Relative Motion in General:
   • The effect depends only on the relative velocity between the source and observer.

Mathematical Representation

The observed frequency $f^{\prime }f’$ is given by:

$f^{\prime }=f\times \frac{v+v_o}{v-v_{\mathrm{s<span\; style="font-size:\; 16px"><span><span></span></span></span><span\; style="font-size:\; 16px">\; </span>}}}$Where:

• $ff$: Frequency of the sound source.
• $vv$: Speed of sound in the medium.
• $v_{o}v\_o$: Speed of the observer (positive if moving toward the source, negative if moving away).
• $v_{s}v\_s$​: Speed of the source (positive if moving toward the observer, negative if moving away).

Real-Life Applications

• Astronomy: Explains the redshift (stretching of light waves) and blueshift (compression of light waves) of stars and galaxies.
• Radar and Sonar: Measures speed (e.g., vehicles, oceanic objects) using sound or electromagnetic waves.
• Medical Imaging: Doppler ultrasound measures blood flow by detecting frequency changes in reflected sound waves.

The Doppler effect explains how motion alters the perceived sound frequency due to the compression or stretching of sound waves. This phenomenon is not only a fundamental concept in wave physics but also a practical tool in various fields.