Class 16, Wednesday,
Several classes ago we discussed how a sound wave propagates through a gas. Last class
we analyzed the displacement and the pressure variation associated with a sound wave.
Here we will focus on the speed
In general, the speed
of any mechanical wave depends on an inertial property
medium (the capacity
of the medium to store kinetic energy), and on an elastic property
(the capacity of the medium to store potential energy). For the wave in a string, the
inertial property is represented by the linear density, while the elastic property is
represented by the tension in the string.
For sound waves, which quantities might play the role
of the tension and linear density?
The inertial property is obviously the mass density. Thinking about our thought-
experiment involving a gas in a long container closed by a piston, the restoring property
must have something to do with the periodic expansion and contraction of a small volume
of the gas. So, pressure and volume must play some role. The physical quantity
that describes the extent
to which a medium changes its volume, !l.V, as the pressure
applied to it varies by an amount !l.P, is called the bulk modulus, B.
B ::; -
It is measured in Pa. We can s:':iaYliqUidS and solids, which are less compressible than
gasses, must have a larger bulk modulus. The sound speed then is:
In solids the sound speed must be larger than in liquids and gasses (for a given density),
because they are less compressible. The material is very resistant to being squeezed, and
furthermore it can communicate this resistance very quickly to whatever is trying to
it This quick feedback results in a large speed
In air the sound speed is 343 mls at 20°C. In gases the sound speed varies with the
temperature. In water it is
and in granite it is
of the sound speed with the temperature in gases can be shown on the
example of an