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Sound Waves in a Fluid

Waves propagate in a fluid much in the same way that a disturbance propagates down a closed hall crowded with people. If one shoves a person so that they knock into their neighbor, the neighbor falls against their neighbor (and shoves back), and their neighbor shoves against their still further neighbor and so on.

Such a wave differs from the transverse waves we studied on a string in that the displacement of the medium (the air molecules) is in the same direction as the direction of propagation of the wave. This kind of wave is called a longitudinal wave.

Although different, sound waves can be related to waves on a string in many ways. Most of the similarities and differences can be traced to one thing: a string is a one dimensional medium and is characterized only by length; a fluid is typically a three dimensional medium and is characterized by a volume.

Air (a typical fluid that supports sound waves) does not support ``tension'', it is under pressure. When air is compressed its molecules are shoved closer together, altering its density and occupied volume. For small changes in volume the pressure alters approximately linearly with a coefficient called the ``bulk modulus'' $B$ describing the way the pressure increases as the fractional volume decreases. Air does not have a mass per unit length $\mu$, rather it has a mass per unit volume, $\rho$.

The velocity of waves in air is given by

\begin{displaymath}
v_a = \sqrt{\frac{B}{\rho}} \approx 343 {\rm m/sec}
\end{displaymath} (161)

The ``approximately'' here is fairly serious. The actual speed varies according to things like the air pressure (which varies significantly with altitude and with the weather at any given altitude as low and high pressure areas move around on the earth's surface) and the temperature (hotter molecules push each other apart more strongly at any given density). The speed of sound can vary by a few percent from the approximate value given above.


next up previous contents
Next: Sound Wave Solutions Up: Sound Previous: Sound Summary   Contents
Robert G. Brown 2004-04-12