B Waves travelling between strings

[WheatNeat]

TL;DR Summary

Why does the relationship between the mass density of the strings determine the phase of the reflected wave?

I just started learning about waves from an introductory calculus-based textbook (HRK) and there was a part describing what happens when a wave on a string transmits into another string (with different mass density). It said that if the wave is going into a string with a larger mass density, the reflected wave has a phase difference of 180 degrees with the original, and a phase difference of 0 if the wave is going into a string with a smaller mass density. But I don't understand why this is the case. I understand that a reflected wave from a foxed point has to have a phase difference of 180 because the fixed point can't have displacement, but I don't understand how it has to be 180 in this case. Why does the relationship between the mass density of the strings determine the phase of the reflected wave?

 

[A.T.]

I understand that a reflected wave from a foxed point has to have a phase difference of 180 because the fixed point can't have displacement, but I don't understand how it has to be 180 in this case. Why does the relationship between the mass density of the strings determine the phase of the reflected wave?

A fixed end is just the limit of mass density ratio going to infinity, while a transversally free end is the limit of mass density ratio going to zero. If you understand what happens in these limits, then you should understand the intermediate cases.

 

[tech99]

Translating from my backgound in radio engineering, the effect observed when a travelling wave reaches the boundary is going to depend on the impedance it is seeing. This depends on the properties of the second string and also whether it is free or fixed at its end and if it goes on for ever.

 

[tech99]

If we are considering just a single pulse, then my answer is not applicable and the reflection will not depend on how the second string is terminated.