2.1. Small Amplitude Wave Assumption

Try these first

1. 1.

   What is the governing equation for wave motion under small amplitude assumptions?

   Hint

   Think about the equations used in fluid dynamics.

2. 2.

   Define celerity in the context of waves.

   Hint

   Consider the relationship between wave length and time.

3. 3.

   What is the primary governing equation used for small amplitude wave analysis?

   • Heat equation
   • Laplace equation
   • Bernoulli's equation

   Hint

   This equation is fundamental in fluid mechanics.

4. 4.

   True or False: Celerity is defined as the ratio of wave height to period.

   • True
   • False

   Hint

   Remember the correct relationship involving wave properties.

5. 5.

   A wave with a wavelength of 12m propagates with a period of 3s in deep water. Derive the celerity and describe how this would change if the water depth were shallow.

   Hint

   Consider how depth affects wave properties.

6. 6.

   Given the dispersion relationship σ² = gk tanh(kd), analyze what happens as k increases while keeping d constant. What physical phenomenon does this relate to?

   Hint

   Reflect on how wave characteristics change with wavelength.