The returning waves will combine with the initial waves to produce patterns of standing waves . Here are some standing waves that can be set up with a string tied down at both ends. Try to think of the pictures as frames of a movie. By changing the initial condition, other standing wave patterns are possible. In music they are called the second, third and fourth harmonics , OR the first, second and third overtones .
Higher harmonics are, of course, possible.
It is easier to visualize standing waves than it is to visualize traveling waves. One need only show the two extreme positions of the vibrating medium. A stretched string vibrates in its 3rd mode with a wavelength of 1.2 meters. It turns out that there are other kinds of standing waves. Consider what happens in a bathtub.