Page 423 - Introduction to Continuum Mechanics

Newtonian Viscous Fluid 407

Therefore, the velocity disturbance

is exactly the same form as the pressure wave.
(c) For the one-dimensional case, we have the following ratio of amplitudes

Thus, the approximation is best when the disturbance has a velocity that is much smaller than
the speed of sound.

Example 6.27.2
Two fluids have a plane interface at x\ = 0. Consider a plane acoustic wave that is normally
incident on the interface and determine the amplitudes of the reflected and transmitted waves.
Solution. Let the fluid properties to the left of the interface (#i<0) be denoted by PI,CI,
c
and to the right (ri>Q) by p2> 2-
Now, let the incident pressure wave propagate to the right, as given by

This pressure wave results in a reflected wave

and a transmitted wave

We must now consider the conditions on the boundary jcj = 0. First, the total pressure must
be the same, so that

or,