17.0 - Introduction
In this chapter, we will discuss what happens when
two or more traveling waves combine with each other,
as when waves meet in a pond, a pool or even a
bathtub. The result is higher peaks and lower troughs.
These waves can “pass through” each other and then
regain their original shape and direction, in contrast to
the collision of two particles, such as tennis balls,
which alters the motion of the balls.
A stringed musical instrument like a violin or a guitar
uses the reflection and recombination of waves from
the end of a bowed or plucked string to create its
magical sound. You also hear the result of waves
combining when you listen to music on loudspeakers
or as a live performance of a band or a symphony. Music halls are designed to take
advantage of the reflection and combination of sound waves to produce an effect
that audience members will find particularly pleasing.
You can begin your study of the result of combining waves with the simulations to
the right. In Interactive 1, you control two wave pulses traveling on the same string.
One pulse starts on the left and moves right, and the other starts on the right and
moves left. You determine the amplitude and width of each pulse, as well as
whether it is a peak or a trough. Set the parameters for each pulse and press GO to
see what happens when the pulses meet. If you want to see the pulses combining in
slow motion, press the “time step” arrow to advance or reverse time in small
increments.
A challenge for you: Can you set the pulses so that when they meet they exactly
cancel each other out, causing the string to be completely flat for an instant?In Interactive 2, two traveling waves combine as they move toward one another.
You determine the amplitudes and wavelengths of these waves. Again, set the
parameters of the waves and press GO to see the result of combining the waves.
Can you create a single combined wave that does not move either to the left or to
the right? If you do, you will have created what is called a standing wave. You will
find that by making the settings of the two waves identical, except for travel
direction, you can create such a wave.Intersecting ripples from two different wave sources in a pond.17.1 - Combining waves: the principle of superposition
In much of this chapter, we discuss what happens
when traveling waves combine. In this section, we
consider the less complicated case of what occurs
when two wave pulses combine in a string, as you
see above. This will help us illustrate the principle of
superposition, which is more readily viewed with
pulses than with traveling waves.Two traveling wave pulses on a string.(^322) Copyright 2000-2007 Kinetic Books Co. Chapter 17