# The Speed of Sound and Doppler Effect

## The Speed of Sound

Sound travels much slower than electromagnetic waves and its speed depends on the medium through which it passes. The greater the density of the material, the greater the speed of sound. This is actually opposite to what happens with light waves, but remember sound is a compressional wave, whereas light is a transverse wave. Since sound needs a medium to propagate, it is compressing material particles together to transmit the energy of the wave.

• vsteel > vwater > vair

• Speed of sound in steel is approximately 5200 m/s, in water about 1500 m/s and in air 331 m/s at 0°C.

• Objects which travel at less than the speed of sound are called subsonic.

• Objects which travel at greater than the speed of sound are called supersonic.

Planes which are traveling at Mach speeds are actually traveling at multiples of the speed of sound. For example, Mach 3 means the plane is traveling at three times the speed of sound in air at that temperature.

## The Doppler Effect

Doppler Effect: The apparent change in frequency due to the movement of observer and/or source.

• If the observer/source are getting closer to each other, the wavelength shortens and the frequency increases, perceived pitch increases.
• If the observer/source are getting further away from each other, the wavelength increases and the frequency decreases, perceived pitch decreases.

We have all observed this effect: Some examples include: driving by a stationary fire whistle, stopped at a railroad crossing as the train passes blowing its whistle. Sometimes people perceive this change as a change in volume, but what is actually going on is a change in the perceived frequency. It is important to remember that the source is NOT actually changing its frequency. It is just that our perception is different.

The equation for Doppler Effect is as follows: f ‘ = f [(v +/- v0)/(v -/+ vs)] where:

v = speed of sound in air at a particular temperature, m/s

vo = speed of the observer, + if motion toward observer, – if motion away from observer, m/s

vs = speed of the source of the sound, + if motion is away from observer, – if motion is toward observer, m/s

f = frequency emitted by the source, in Hz

f ‘ = perceived frequency due to Doppler Effect, in Hz

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