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Standing waves in a string: the speed with which the wave travels does not depend on the vibration that causes the wave, but on the properties of medium. In the case of string, the speed depends on the tension of the string and the mass per unit length. The vibration does affect the wavelength of the wave.
Let us consider a length of string attached at one end to a vibrating object and at the other end to a fixed point a distance L away.
We will assume that point A is vibrating with an amplitude small enough so that A can be considered a fixed point, and that a wave reflected at B will not have diminished amplitude.
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