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# Doppler Effect

## Waves emitted from a moving source are perceived are perceived at a higher or lower frequency by a stationary observer.

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Sonic Boom

### Sonic Boom

Credit: Official U.S. Navy Page
Source: http://www.flickr.com/photos/usnavy/5815021932/

Created by objects that travel through air at a velocity faster than the speed of sound, sonic booms have been known to shake houses, knock over objects and break windows.

#### Amazing But True

• The doppler shift is an effect that happens when a wave source or a receiver move relative to one another. When a wave source approaches a receiver the frequency heard increase and when the source moves away it decreases. The Doppler effect is best represented as

\begin{align*}f = f_\circ \left(\frac{v \pm v_r}{v \pm v_s}\right) \end{align*}

where \begin{align*}v\end{align*} is the speed of sound, \begin{align*}v_r\end{align*} is the speed of the receive and \begin{align*}v_s\end{align*} is the speed of the source. \begin{align*}v_r \end{align*} and \begin{align*}v_s\end{align*} is positive when the source/receiver is moving towards one another and negative when they are moving apart.

• Credit: Arup Malakar
Source: http://www.flickr.com/photos/amalakar/8747066225/

Sounds waves from a car's horn increases as it moves toward the reciever and decreases as the passes [Figure2]

• To understand when a sonic boom is created, you would look at what happens when the wave source travels faster than the speed of sound. When the source moves with a speed that is greater than the speed of sound, no waves will move in front of the source. As a result, the waves pile up behind the source to form a shock wave.

#### Show What You Know

1. If the receiver moves away from the source at a speed that is greater than the speed of sound, what happens?
2. If the receiver and the source move in the same direction at the same velocity, how is the frequency shifted?
3. Would you expect the build up of sound waves behind an air craft that travels greater than the speed of sound to be compression waves of higher pressure or lower pressure?