Finding the magnitude of the nearest peak and period

AI Thread Summary
The discussion focuses on solving a problem related to a harmonic wave described by the equation h(x,t)=cos(2π(2x-t/2)). The first part of the question seeks the wavelength, while the second part asks for the period of the wave. Participants clarify that the wavelength and period can be derived from the simplified equation cos(4π(X-t/4)). Key insights include the importance of understanding the wave's movement and how to extract values from the general wave equation. The conversation emphasizes the relationship between the wave's parameters and the need for careful analysis to distinguish between them.
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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!
 
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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 :)
 
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!
 
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.
 
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