# Finding the magnitude of the nearest peak and period

1. Jan 27, 2012

### apbuiii

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
Period=2∏/B; Acos(B(X-D))

3. 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.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jan 28, 2012

### Simon Bridge

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 travelling wave at t=0, so at t>0 ... you can take it from here :)

3. Jan 28, 2012

### 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!

4. Jan 29, 2012

### 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.