Q19DQ - University Physics with Modern Physics

Question

As we discussed in Section 15.1, water waves are a combination of longitudinal and transverse waves. Defend the following statement: “When water waves hit a vertical wall, the wall is a node of the longitudinal displacement but an antinode of the transverse displacement.”

Step-by-Step Solution

Answer

The statement “when water waves hit the vertical wall, the wall is a node of the longitudinal displacement but an antinode of the transverse displacement." is justified. 

STEP 1: Concept of water wave .

The longitudinal and transverse waves combine to form a water wave. When a wave of water strikes a wall, the longitudinal displacement amplitude is zeroed out while the transverse displacement amplitude moves to its maximum point.

Step 2 Relation of water wave with a longitudinal and transverse wave.

For longitudinal waves, the waves hit the wall and disappear that is there is no further longitudinal displacement of waves can take place and hence the amplitude becomes zero. Thus, the wall acts as a node. 

For transverse waves, whose displacement is perpendicular to the water surface, the waves hit the wall, the amplitude of the wave gets to its maximum wave since the vertical wall does not offer any impedance to the transverse motion of the wave and hence, hence the wall act like antinodes for transverse displacement  

 

Therefore, the statement “when water waves hit the vertical wall, the wall is a node of the longitudinal displacement but an antinode of the transverse displacement." is justified.