M3Q4

A wave with height of 4m and period of 9s is approaching the coastline at an angle of about 14 degrees. Would the period change when approaching the beach?

Question

M3Q4

A wave with height of 4m and period of 9s is approaching the coastline at an angle of about 14 degrees. Would the period change when approaching the beach?

BlackTom AI · Accepted Answer

Question restatement: A wave with height 4 m and period 9 s approaches the coastline at a 14-degree angle. The question asks: would the period change as the wave approaches the beach?

Option 1: Yes, the period changes due to refraction and shoaling.
- Refraction and shoaling describe changes in direction, wave height, and wavelength as waves move into shallower water, but the fundamental wave period (the time between consecutive crests passing a fixed point) generally remains constant for non-dissipative water waves. Refraction alters the wave direction and wavelength, while shoaling increases height and decreases wavelength; neither concept inherently requires a change in period. Therefore this statement is incorrect.

Option 2: Yes, the period changes as waves slow down.
- While wave speed decreases in shallower water, the period is not dictated by speed in non-dispersive shallow-water waves. For typical ocean waves, the frequency (and thus the period) is conserved as they transition to shallower depths; the slowing down does not force a change in period. This makes the statement incorrect. A common misconception is to equate slower speed with a different time between crests, which isn’t the case here.

Option 3: No, the period does not change because waves are not dispersive in shallow water.
- In shallow water, long waves can be approximated as non-dispersive, meaning phase speed is nearly independent of frequency and the period remains essentially constant as depth decreases. This aligns with the general understanding of wave behavior: shoaling and refraction modify height and direction, but not the period. This statement is correct in spirit, though the wording about non-dispersive shallow water is the key justification.

Option 4: No, the period does not change as this would means the number of waves at one point and at unit time should change.
- This option also asserts that the period does not change, but then provides a justification that ties period to the number of waves per unit time. Since period is inversely related to frequency (and thus to the rate at which crests pass a point), saying the number of waves per unit time should change would actually imply a change in period, making the logic here flawed or at least inconsistent with the premise (constant period). The reasoning is muddled and not a reliable justification for period constancy.

Summary cross-check: The scientifically supported view is that, as waves move into shallower water, their speed and wavelength change while the period remains approximately constant. This aligns with Option 3 being the most accurate statement, while Options 1 and 2 attribute period changes that are not expected for non-dispersive shallow-water waves, and Option 4 contains inconsistent reasoning about wave frequency versus period.

M3Q4 A wave with height of 4m and period of 9s is approaching the coastline at an angle of about 14 degrees. Would the period change when approaching the beach?单项选择题

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