- #1
unscientific
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Homework Statement
Homework Equations
The Attempt at a Solution
i have no clue about the second part..
Click For Summary
Homework Help Overview
The discussion revolves around understanding waves in a dispersive medium, specifically focusing on the implications of superimposing waves with different wavelengths and the resulting group and phase velocities.
Discussion Character
- Exploratory, Mathematical reasoning, Assumption checking
Approaches and Questions Raised
- Participants explore the concept of superimposing waves with varying wave numbers and angular frequencies, questioning how to prove relationships between group velocity and phase velocity under different conditions.
Discussion Status
Some participants are attempting to derive expressions related to wave behavior in dispersive media, while others express uncertainty about their approaches and seek clarification on specific calculations and assumptions.
Contextual Notes
There appears to be confusion regarding the conditions under which certain approximations hold, particularly in relation to the parameters h, k, and λ. Participants are also grappling with the implications of their assumptions on the results they are obtaining.
i have no clue about the second part..
- #2
unscientific
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bumpp
- #3
unscientific
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Am I suppose to superimpose the following waves:
exp i(kx - wt) + exp i((k+Δk)x - w't)
whereby the other wave has a different wavelength such that k becomes k+Δk and w becomes w' (with k+Δk) ?
So I found that at h >> 1/k or h >> λ/2∏
vg = (1/2) vg
And at h << 1/k or h << λ/2∏
vg ≈ vpI first assume that h >> 1/k or h >> λ/(2∏): But how do i prove this? I can't seem to solve the tanh function to find the value of k..
I got:
0.16≈k*tanh(1000k)
If i assume k≈0.16 since tanh(160) ≈ 1..
i get vp = 7.9m/s
Time taken = 35 hours..
exp i(kx - wt) + exp i((k+Δk)x - w't)
whereby the other wave has a different wavelength such that k becomes k+Δk and w becomes w' (with k+Δk) ?
So I found that at h >> 1/k or h >> λ/2∏
vg = (1/2) vg
And at h << 1/k or h << λ/2∏
vg ≈ vpI first assume that h >> 1/k or h >> λ/(2∏): But how do i prove this? I can't seem to solve the tanh function to find the value of k..
I got:
0.16≈k*tanh(1000k)
If i assume k≈0.16 since tanh(160) ≈ 1..
i get vp = 7.9m/s
Time taken = 35 hours..
Last edited:
- #4
unscientific
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bumpp
- #5
unscientific
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bumpp anyone?
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