Let us describe pictorially the motion of a one-dimensional longitudinal pulse moving
through a long tube containing a compressible gas (Fig. 17.1). A piston at the left end
can be moved to the right to compress the gas and create the pulse. Before the piston is
moved, the gas is undisturbed and of uniform density, as represented by the uniformly
shaded region in Figure 17.1a. When the piston is suddenly pushed to the right (Fig.
17.1b), the gas just in front of it is compressed (as represented by the more heavily
shaded region); the pressure and density in this region are now higher than they were
before the piston moved. When the piston comes to rest (Fig. 17.1c), the compressed
region of the gas continues to move to the right, corresponding to a longitudinal
pulse traveling through the tube with speed v. Note that the piston speed does not
equal v. Furthermore, the compressed region does not “stay with” the piston as the
piston moves, because the speed of the wave is usually greater than the speed of the
piston.
The speed of sound waves in a medium depends on the compressibility and density
of the medium. If the medium is a liquid or a gas and has a bulk modulus B (see