unscientific
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Homework Statement
Homework Equations
The Attempt at a Solution
i have no clue about the second part..
4 replies · 2K views · last reply
i have no clue about the second part..
Discussion
unscientific
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bumpp
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) ?
![Three equations: y1 = A sin[(k + Δk)x - (ω + Δω)t], y2 = A sin[(k - Δk)x - (ω - Δω)t], and their sum y = y1 + y2 = 2A cos(Δk x - Δω t) sin(kx - ωt).](https://www.physicsforums.com/attachments/op66g-png.160617/ "op66g.png")
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:
unscientific
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bumpp
unscientific
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bumpp anyone?