3. Group Celerity

Try these first

1. 1.

   What is group celerity?

   Hint

   Think about how a group behaves differently from an individual.

2. 2.

   How does phase velocity differ from group velocity?

   Hint

   Consider their definitions and how they relate to wave behavior.

3. 3.

   What is the relationship between group velocity and phase velocity in deep water?

   • Group velocity is equal to phase velocity
   • Group velocity is half of phase velocity
   • Group velocity is twice the phase velocity

   Hint

   Think about how energy disperses across waves.

4. 4.

   True or False: Group Celerity increases in shallow water.

   • True
   • False

   Hint

   Consider the definition of group velocity.

5. 5.

   A coastal engineer needs to build a structure that can withstand waves with a phase speed of 12 m/s in deep water. What is the required group celerity?

   Hint

   Use the formula C_G = C / 2.

6. 6.

   Discuss how the change from deep to shallow water impacts the wave energy transfer. Explain with respect to group celerity.

   Hint

   Consider the implications this change has for coastal engineering.