Practice Famous Dispersion Relationship (2.4) - Velocity Potential Derivation

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6 sample questions

Question 1.
Define wave celerity.
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Think about how you calculate speed in general.
Question 2.
What does the dispersion relationship relate in wave mechanics?
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Consider the main parameters that affect wave characteristics.
3Question 3.
What does the dispersion relationship express?
- Wavelength and period relationship
- Wave energy
- Fluid potential
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Think about how waves travel in fluids.
4Question 4.
True or False: Wave celerity decreases with increasing water depth.
- True
- False
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Remember the effect of depth from the dispersion equation.
Question 5.
A wave travels at a water depth of 10 meters. How would the dispersion relationship change if the depth is increased to 30 meters? Explain.
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Consider how the function tanh behaves with increasing values of k and d.
Question 6.
Given a period of a wave is 4 seconds and using the dispersion equation, derive the wavelength required for a given water depth of 5m.
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First, calculate k then backtrack to find the wavelength.

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