Problem 14 - University Physics with Modern Physics

Question

A ping-pong ball is floating in the middle of a lake and waves begin to propagate on the surface. Can you think of a situation in which the ball remains stationary? Can you think of a situation involving a single wave on the lake in which the ball remains stationary?

Step-by-Step Solution

Answer

Explain the general and specific situation involving multiple waves and a single wave. Answer: It is possible for a ping-pong ball floating on a lake with propagating waves to remain stationary if there are multiple waves interfering with each other, causing constructive and destructive interferences to perfectly cancel each other out, leading to a zero net disturbance at the position of the ball. However, in the specific situation where there is only a single propagating wave, the ball cannot remain stationary, as it will move upward during a wave crest and downward during a trough. For the ball to remain stationary, multiple waves are necessary to create a balanced disturbance.

Step 1: General Situation: Multiple Waves

Consider a scenario where waves travel outward from different points on the lake and their amplitudes, frequencies, and directions are different. It is possible that these waves may interfere with each other, causing the ping-pong ball to remain stationary. This can happen when constructive and destructive interferences cancel each other perfectly, leading to a zero net disturbance at the position of the ball. In this case, the ball remains stationary.

Step 2: Specific Situation: Single Wave

Now, let's consider the case where there's only a single wave propagating on the surface of the lake. Since a ping-pong ball is light enough, it will follow the wave motion without any resistance. If a wave crest reaches the ball, it will move upward, and when a trough reaches the ball, it will move downward. In this case, it's impossible for the ball to remain stationary with only a single propagating wave. For the ball to remain stationary, we need multiple waves interfering with each other to create a balanced disturbance, as discussed in the general situation.