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Nathanael

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The speed of the wave depends on the tension in and density of the rope. So the medium determines the speed of the wave, but there are infinite combinations of frequency and wavelength that will give the correct speed.

For a given rope under a given tension, the wave will travel at a certain speed and the wavelength will depend on the frequency according to [itex]\lambda=\frac{v}{ƒ}[/itex].

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The source does not play any role in wave speed other than through the fact that some media have dispersion relations such that the wave velocity is frequency dependent. The relation v = λf can rather be thought of as relating the frequency and wave length for a given wave velocity, i.e., for a wave with wave velocity v, a wave of frequency f will have wave length λ = v/f. Of course, if you measure the wave length and frequency, you can infer what the velocity is (and thus obtain information on the internal properties of the medium).

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