Speed of Sound

Another important consequence of the compressibility of fluids is that disturbances introduced at some point in the fluid propagate at a finite velocity. For example, if a fluid is flowing in a pipe and a valve at the outlet is suddenly closed, creating a localized disturbance, the effect of the valve closure is not felt instantaneously upstream. It takes a finite time for the increased pressure created by the valve closure to propagate to an upstream location. It takes a finite time for the increased pressure created by the valve closure to propagate to an upstream location.

Similarly, a loudspeaker diaphragm causes a localized disturbance as it vibrates, and the small change in pressure created by the motion of the diaphragm is propagated through the air with a finite velocity. The velocity at which these small disturbances propagate is called the acoustic velocity or the speed of sound, $c$.

The speed of sounds is related to changes in pressure and density of the fluid medium through the equation

$$c=\sqrt{\frac{dp}{d\rho }}$$

or in therms of the bulk modulus by

$$c=\sqrt{\frac{E_v}{p}}$$

For ideal gases, we have

$$c=\sqrt{kRT}$$

Some speeds of sound:

$$\begin{array}{rl}{c}_{\text{air}}& =340\text{ m/s}\\ c_{\text{water}}& =1500\text{ m/s}\end{array}$$