Waves - General question about Damping and how it affects a propagating wave

[jerad908]

Homework Statement

How does changing the damping affect other characteristics of a wave?

Relevant Equations

none

I think increasing the damping would decrease the amplitude and increase the Period (T). But, what I'm really unsure about is the frequency, wavelength and wave speed. Would it be no effect on those three? Because if dampening acts like friction, wouldn't it slow down the wave/ increase speed?

 

[Merlin3189]

It depends on whether you are talking about the wave, or the oscillator which generates the wave.

An undamped wave $A sin(\omega t + \phi )$ becomes a damped wave when multiplied by an exponential decay term to give $\exp ^{-kt} A sin(\omega t + \phi )$

Then the frequency and wavelength must be the same, since the sine term will be zero at the same places and I'm assuming the speed of propagation is the same, as for EM waves in free space.
The amplitude obviously decreases as multiplied by the decreasing exp term.

But waves arise (inter alia) from simple harmonic oscillators. The sine function is the solution to the differential equation for the oscillator. When damping is added, the equation is changed and the solution is not quite so simple. For things like pendulum, spring-mass, LCR circuit, the effect of damping is to slow the oscillation and therefore increase the period. So the generated waves have longer period and lower frequency as well as the obvious decreasing amplitude.
I can't give more than that general qualitative point. Await experts for more.

Things get even more out of my depth in dispersive media or where the medium itself is causing the damping.
A damped wave is clearly no longer a single frequency sine wave. It is modulated and must contain lower frequency components, each of which can be affected differently by the medium.