0
$\begingroup$

I am reading Griffiths' Intro to Electrodynamics (Section 9.1.3 Boundary Conditions: Reflection and Transmission) where he analyzes the case of an incident wave sent down a string that is tied to another string. The first string has uniform mass per unit length $\mu_1$ and the second has uniform mass per unit length $\mu_2$.

He says the incident wave is a sinusoidal oscillation that extends (in principle) all the way back to $z=-\infty$ (defining $z$ the axis along the length of the string) and that the same goes for the reflected wave and transmitted wave (except $z=+\infty$ for the transmitted wave).

I'm not entirely sure what's confusing me, but I'll start with this question:

What guarantees that the transmitted and reflected waves are sinusoidal?

$\endgroup$
0

1 Answer 1

0
$\begingroup$

Keep in mind that the boundary condition (e.g. the reflector) is merely an idealistic model. If the reflector is non-linear, then the boundary condition is also non-linear and may lead to harmonics (whose characteristics depend upon the true characteristics of the reflector, the amplitude of the incident wave, etc), leading to a reflection that isn't necessarily purely sinusoidal.

As the string permits propagation in both directions (towards and away from the wave source), the boundary condition (e.g. the reflector) represented by the (implied idealistic) model constrains the reflected/incident/transmitted sinusoidal waves.

See also: Is a reflected wave on a string of the same form as of the incident.

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.