Question

If a friend tells you that if a water wave travels at 155 mph across the deep ocean, the water in the wave must be moving at least this fast, how might you respond?

Answer 1

Water waves' speed refers to the propagation speed, not the speed of individual water molecules. To determine ocean depth using a ship's sonar, multiply the travel time of the signal by the speed of sound in sea water and divide by two since the signal travels to the ocean bottom and back.

Step-by-step explanation:

If a water wave travels at 155 mph across the deep ocean, it does not mean that the water itself is moving at this speed. The speed of the wave refers to the propagation speed at which the wave shape moves across the ocean.

This is different from the speed at which individual water particles move, which is generally much slower and involves motion mostly in vertical circles as waves pass. In contrast, the motion of objects on the surface, like a seagull, is not at the constant speed of wave propagation, but instead they bob up and down with the passing waves.

To determine the depth of the ocean using a ship's sonar, one would consider the time it takes for a signal to travel to the ocean bottom and back. The speed of sound in seawater is typically around 1450 m/s

. If a signal is received 1.5 seconds after being sent, the total distance covered by the signal would be 1.5 seconds multiplied by 1450 m/s. Since the signal travels to the bottom and back up, the depth is half of this distance. Therefore, to calculate the depth you divide the total distance by 2.

Example calculation for the depth of the ocean:

1. Total travel time of the signal: 1.5 seconds
2. Speed of sound in sea water: 1450 m/s
3. Total distance traveled by the signal: 1.5 seconds × 1450 m/s
4. Depth of the ocean: (Total distance traveled by the signal) / 2