Solving Deep Water Wave Dispersion for Storm Distance

[ambientdream]

Homework Statement

: The dispersion relation for long-wavelength surface waves in
deep water is ω=(gk)^1/2 . Waves of a fixed wavelength (or period) travel at their group velocity.
Surface waves generated by a storm in the mid-Atlantic and having a period of 15 seconds arrive at
the British coast at noon Monday. By noon Tuesday, the period of the waves arriving at the coast has dropped to 13 seconds. How far away did the storm occur?

Homework Equations

ω=(gk)^1/2

The Attempt at a Solution

No idea how to start. Please help :)

 

[ehild]

Waves of different periods travel at different group velocity. So they arrive at the cost from the place where the storm occurred at different time. How is the group velocity defined?

ehild

 

[ambientdream]

The group velocity is defined as follows v=(1/2)(g/k)^(1/2). How would you start calculating how far away the storm is?

 

[ehild]

You know the time period, determine ω. Knowing ω, you find k, knowing k you get the group velocity for both frequencies. The time needed for a wave to arrive from distant x is x/v.
The time delay between the arrival of the two kind of waves is one day. Can you write up am equation for x?


ehild