Solving Deep Water Wave Dispersion for Storm Distance

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Homework Help Overview

The problem involves understanding the dispersion relation for long-wavelength surface waves in deep water, specifically relating to waves generated by a storm and their travel to the coast over time. The context includes calculating the distance from the storm based on the change in wave period observed at the coast.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the definition of group velocity and its implications for wave travel time. There are attempts to relate the time periods of the waves to their respective group velocities and the distance from the storm.

Discussion Status

Some participants have provided definitions and relationships between wave properties, while others are exploring how to set up equations based on the information given. There is an ongoing exploration of how to calculate the distance based on the time delay between wave arrivals.

Contextual Notes

The problem involves specific wave periods and their relationship to group velocity, with a focus on the time delay between different wave types arriving at the coast. The discussion reflects uncertainty in how to initiate calculations based on the provided equations and definitions.

ambientdream
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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 :)
 
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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
 
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?
 
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
 

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