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

insertnamehere

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?

Tom Mattson

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 [itex]v_1=\lambda_1f_1[/itex] and [itex]v_2=\lambda_2f_2[/itex], so what can you say about the wavelengths?

insertnamehere

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

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.

The wave speed decreases as you move to the string of higher mass density.

insertnamehere

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