Finding the magnitude of the nearest peak and period

[apbuiii]

Homework Statement

Harmonic wave is described by: h(x,t)=cos(2∏(2x-t/2)). The equation is expressed as the height of the wave

At time t₀ a peak of the wave is at position X₀. What is the magnitude of the distance to the nearest peak at this time? How much time passes before another peak is observed at that postion?

Homework Equations

Period=2∏/B; Acos(B(X-D))

The Attempt at a Solution

I figured that the first part of the question is asking the wavelength and the second part of the question is finding the period. I simplified the equaiton to cos(4∏(X-t/4)). I don't really know how to distinguish the wavelength from the period from the given equation. They both make sense to equal 1/2.

Thanks for your help in advance!

 

[Simon Bridge]

I figured that the first part of the question is asking the wavelength and the second part of the question is finding the period.

That would be correct :)

Consider the general case: some pulse has a height function f(x) at t=0 - we write: h(x,0)=f(x) ... no brainer really. But if it moves to the right at speed v, then at time t it has moved a distance vt and we have to write:
h(x,t)=f(x-vt)

This is key to what you want to know!

Imagine f(x)=Acos(kx) ...this is your traveling wave at t=0, so at t>0 ... you can take it from here :)

 

[apbuiii]

Ah, I see what you're saying and I am taking what you left there for me :) Haha. I guess the introduction of two variables at a time confused me haha. One thing at a time... Thank you!

 

[Simon Bridge]

Good - since you took the trouble to simplify your equation, once you have expanded the general equation for h(x,t) you can just read-off k and v and use them to get the values you need.