What is the amplitude of a wave transmitted from dense to light string?

[salsero]

A string has two parts: one with a very high mass density (per unit length), and the other with a very low mass density. A wave with amplitude A moves from the dense part toward the light part. What will be the amplitude of the wave which is transmitted to the light part?

 

[Integral]

This will depend on the different densities of the strings. There will be some transmission and some reflected energy. To get the exact ratio it would be necessary to solve a double wave equation system. with a boundary condition at connection point be that their displacement be the same for all time.

This problem may be solved is some textbooks. If you have access to a university liberary you may want to search the Partial Differential Equation text for a solution.

 

[salsero]

I am interested in the limit where the ratio of the densities of the heavy part and the light part is very large (infinite).

Probably the answer to this limiting case can be found without solving differential equations...

 

[birdus]

I may be wrong but I don't think the amplitude will change, but the frequency between the two part will. Isn't energy a product of frequency? E=hv

 

[Integral]

Originally posted by birdus
I may be wrong but I don't think the amplitude will change, but the frequency between the two part will. Isn't energy a product of frequency? E=hv

This is not a Quantum Mechanics problem, hν has nothing to do with it.

In the limit you speak of the result would be the same as a wave equation with a free end boundary condtion. This should be a easy solution to find in most PDE texts.