- #1
unscientific
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Homework Statement
Homework Equations
The Attempt at a Solution
i have no clue about the second part..
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The discussion revolves around understanding wave behavior in a dispersive medium, particularly focusing on the superposition of waves with different wavelengths. The user is attempting to analyze the relationship between group velocity (vg) and phase velocity (vp) under varying conditions of wavelength and wave number. They express confusion about proving certain relationships involving the hyperbolic tangent function and its implications for wave propagation. The user arrives at an approximate value for the wave number (k) and calculates a phase velocity but seeks further clarification on their approach. The conversation highlights the complexities of wave dynamics in dispersive media and the challenges faced in solving related equations.
i have no clue about the second part..
- #2
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bumpp
- #3
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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
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bumpp
- #5
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bumpp anyone?
for d), I am a bit confused. I have two trains of thoughts here
any thoughts on which answer is correct, and why the other one is incorrect? Both seem like valid solutions to me. Or is the question ambiguous?
thanks
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