Wave problem

[tinksy]

I have a question regarding waves which has been bugging me for a while:

"You are given a travelling wave with an equation of the form
cos(ax+/-bt)
where x and t are position and time as usual, a and b are positive numbers. Explain how you would physically determine the direction that the wave is travelling in"


Here are my ideas:

I'm assuming that we only need to determine the 'direction' ie positive or negative direction in which the wave is traveling, so it's one dimensional. This means we can use the Doppler Effect. If we choose an arbitrary direction on the line to travel, the direction which gives an apparently lower frequency than expected is going away from the source, and the direction which gives a higher frequency is going towards the source. Since the wave always travels away from the source, we can determine the direction of wave propagation.

Is this right?

[Tom Mattson]

The Doppler effect is one way to do it, but don't forget that if we are talking about something other than light waves, we have to transform the velocity of the wave as well.

A more straightforward way of doing it would be to note that, for plane waves, the phase of the wave is a constant. From this, we can deduce the direction of the wave velocity.

y(x,t)=cos(kx+ωt)
kx+ωt=constant
k(dx/dt)+ω=0
dx/dt=-ω/k

Since dx/dt<0, this wave is traveling in the negative x-direction.

y(x,t)=cos(kx-&omega;t)
kx-&omega;t=constant
k(dx/dt)-&omega;=0
dx/dt=+&omega;/k

Since dx/dt>0, this wave is traveling in the positive x-direction.

[tinksy]

cheers tom [:)]

so would that be considered a physical way of determining the direction of the wave???

[Tom Mattson]

Yes, it would--but so would yours.

The difference is, my way would be considered the easy way! [;)]