Figure 9.3: Colliding wave pulses. (a) Before the collison. (b) During the collision, the wave pulses overlap,
and amplitudes add algebraically. (c) After the collision, the wave pulses have passed through each other
unchanged.
a bigger wave. This situation is calledconstructive interference—the waves add together constructively. On
the other had, if the waves overlap and their displacements are in theoppositedirection, the two waves will
tend to cancel each other out, resulting in a smaller wave (or even no wave at all). This situation is called
destructive interference.
An example of wave interference is shown in Fig. 9.4. The figure shows two wave pulses of the same
size and shape headed toward each other. Fig. 9.4(a) shows constructive interference, and Fig. 9.4(b) shows
destructive interference. Notice something interesting that happens in the case of destructive interference:
although the waves momentarily cancel completely and leave no wave at all, the particles in the string are
still in motion, so new waves will emerge from the flat string and continue on their way.
9.7 Wave Energy.
Waves carry energy, but not mass. Each particle of the wave medium oscillates in place around its own
equilibrium position, so no mass is transported. The wave disturbance does move, though, and carries energy
with it. How much energy does a wave transport?
Suppose we have a harmonic wave traveling through a medium. Each particle of the medium oscillates
with simple harmonic motion, and has energyE DkA^2 =2, wherekis the spring constant andAis the
amplitude. By Eq. (5.7), we know the spring constant is related to the frequency bykDm!^2. Substituting
this into the expression for energy gives
ED^12 m!^2 A^2 : (9.9)Now if the wave has surface areaSand moves with velocityv, then in timetit will sweep out a volumeSvt.
Since the massmof a small volume of the medium is the mass divided by the volume, we havemD Svt,