2.4. Famous Dispersion Relationship

Try these first

1. 1.

   Define wave celerity.

   Hint

   Think about how you calculate speed in general.

2. 2.

   What does the dispersion relationship relate in wave mechanics?

   Hint

   Consider the main parameters that affect wave characteristics.

3. 3.

   What does the dispersion relationship express?

   • Wavelength and period relationship
   • Wave energy
   • Fluid potential

   Hint

   Think about how waves travel in fluids.

4. 4.

   True or False: Wave celerity decreases with increasing water depth.

   • True
   • False

   Hint

   Remember the effect of depth from the dispersion equation.

5. 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.

   Hint

   Consider how the function tanh behaves with increasing values of k and d.

6. 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.

   Hint

   First, calculate k then backtrack to find the wavelength.