# Wave dispersion and the bandwidth theorem

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1. Apr 14, 2015

### RYANDTRAVERS

1. The problem statement, all variables and given/known data
Consider a propagating wave packet with initial length L0.
Use the bandwidth theorem to show that the minimum range of angular frequencies present in the wave packet is approximately:

\Delta \omega = \frac{v_{g}}{L_{0}}

where vg is the group velocity.
2. Relevant equations
The dispersion relationship for the wave is:

\omega ^{2} = gk

3. The attempt at a solution
attached as photo along with original problem sheet. For some reason I get the answer as:

\Delta \omega = 2\pi \frac{v_{g}}{L_{0}}

see method attached.

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Last edited: Apr 14, 2015
2. Apr 15, 2015

### Delta²

Yes i agree with your result. but how exactly have you been taught the bandwidth theorem? I just know it as $\Delta k\Delta x\approx 2\pi$ where $\Delta k , \Delta x$ are defined properly.

Last edited: Apr 15, 2015
3. Apr 15, 2015

### RYANDTRAVERS

Well, yeah we defined it as $$\Delta k \Delta x = 2\pi$$ and then the rest can be derived from there.

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