1.4. Amplitude of the Wave and Wave Propagation

Try these first

1. 1.

   What is the formula for wave celerity?

   Hint

   Think about how wavelength and time relate to the speed of waves.

2. 2.

   Define velocity potential.

   Hint

   Consider the energy of the wave movement.

3. 3.

   What determines the wave celerity?

   • Amplitude and time period
   • Wavelength and time period
   • Frequency and height

   Hint

   Consider what parts of a wave influence its speed.

4. 4.

   True or False: The dispersion relationship indicates wave speed is independent of water depth.

   • True
   • False

   Hint

   Reflect on how depth influences wave dynamics.

5. 5.

   Derive the equation for celerity as a function of water depth using the dispersion relationship, σ² = gk tanh(kd). Show your workings and discuss how this relates to real-world wave behavior.

   Hint

   Utilize the fact that k = 2π/L when expressing L.

6. 6.

   Explain how the phase of a wave changes in shallow vs. deep water and derive the impact on the wave's observable behavior.

   Hint

   Consider the effects of friction and bottom interactions as depth decreases.