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RYANDTRAVERS
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Homework Statement
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:
\begin{equation}
\Delta \omega = \frac{v_{g}}{L_{0}}
\end{equation}
where vg is the group velocity.
Homework Equations
The dispersion relationship for the wave is:
\begin{equation}
\omega ^{2} = gk
\end{equation}
The Attempt at a Solution
attached as photo along with original problem sheet. For some reason I get the answer as:
\begin{equation}
\Delta \omega = 2\pi \frac{v_{g}}{L_{0}}
\end{equation}
see method attached.
Attachments
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