# Waves in dispersive medium

1. Apr 9, 2013

### unscientific

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

2. Relevant equations

3. The attempt at a solution

i have no clue about the second part..

2. Apr 10, 2013

### unscientific

bumpp

3. Apr 12, 2013

### unscientific

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 ≈ vp

I 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: Apr 12, 2013
4. Apr 15, 2013

### unscientific

bumpp

5. Apr 17, 2013

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bumpp anyone?