waves on strings

[Jeff85]

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There are 2 seemingly contradictory statements made in my books:

1. From PR, they say if you have the beginning part of a string heavier than the end part, frequency remains the same because you're entering a different medium(and velocity increases and wavelength increases)
2. From my College textbook, they say you tune a piano or guitar by increasing/decreasing the mass of the string, thus changing the frequency(because of the change of wave speed).

So...why would in one case (heaving part of string to lighter part of string) the frequency be held constant and in the other case(we have one constant spring mass after changing) we keep the wavelength constant?
Why does it matter that you suddenly entered the lighter part of the string and not started out there?

 

[Isoprop]

They are both true but for different cases. The first case talks about a propagating wave. The frequency of a propogating wave is always going to be the same as we enter different mediums. So the velocity changes.

For the guitar, we are talking about standing waves. As we change the tension, we change the mass (or the linear density) of the string. The frequency is determined by the wavespeed of a standing wave.