# Will the wavelength decrease when the wave moves from a light string to a heavy

hi, i was just wondering if a wave's wavelength will change when it goes from a light string to a heavier one. I think it wouldn't affect it, however I know that velocity will be affected as the linear density will be changed. But am I right, will the wavelength remain unaffected?

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Tom Mattson
Staff Emeritus
Gold Member
You're right that the speed changes. It seems that the essential piece of information that you are missing is this: the frequency does not change.

So since you know that $v_1=\lambda_1f_1$ and $v_2=\lambda_2f_2$, so what can you say about the wavelengths?

ok, so that means that although the mass of the string increases, this will have no affect whatsoever on the frequency because since
v= sqrt(T/linear density) and also (wavelength/tension)
and increasing the mass of the string will have no affect on the tension, v increases as the tension remains constant, therefore will the wavelength have to INCREASE in order to compensate the equation? Am i on the right track?

Tom Mattson
Staff Emeritus
Gold Member
insertnamehere said:
v= sqrt(T/linear density) and also (wavelength/tension)
The first part is right, but the second part is not. v does not equal (wavelength/tension). That expression doesn't even have the right units to be a speed.

and increasing the mass of the string will have no affect on the tension, v increases as the tension remains constant, therefore will the wavelength have to INCREASE in order to compensate the equation? Am i on the right track?
The wave speed decreases as you move to the string of higher mass density.

oh no, i meant v= (wavelength/PERIOD)