2022 A/L Physics Past Paper · Question 21 (English Medium)

Answer: (2) Only (B) is true.

What the question asks

We want: which of the statements (A), (B), (C) are true for a tsunami wave in deep water compared with shallow water.

What each letter means:

$\lambda$ ($\text{m}$): the wavelength, the distance from one crest to the next.

$v$ ($\text{m s}^{-1}$): the speed of the wave.

$a$ ($\text{m}$): the amplitude, the height of a crest above the calm water level.

Relevant theory

The velocity (v) of the tsunami wave decreases when reaching the sea shore. 2. The wavelength ( ) λ too of the wave decreases. 3. But the amplitude (a) of the wave increases.

Reading the options

The options are combinations of (A), (B), (C).

We check each statement on its own.

The theory above tells us what happens when the wave runs in towards the shore. For deep water we read each change the other way round.

For example, think of a wave rolling onto a beach. Far out it is long, low and fast. Near the sand it slows down, bunches up into shorter lengths and rises into a taller wave.

So each change near the shore goes the opposite way in deep water.

Reasoning and calculation

Wavelengths of waves in deep water are lower than that in shallow water.

Near the shore the wavelength gets shorter. So in deep water it is longer. It is not lower.

A

Speeds of waves are higher in deep water than that in shallow water.

Near the shore the speed decreases. So in deep water the speed is higher.

B

Amplitudes of the waves in deep water are higher than that in shallow water.

Near the shore the amplitude increases. So in deep water it is smaller. It is not higher.

C

(A) is false: the wavelength is longer in deep water.

(B) is true: the speed is higher in deep water.

(C) is false: the amplitude is smaller in deep water.

So only (B) is true.

Why the other options fail

(A) is false. The wavelength gets shorter near the shore, so it is longer in deep water.

(A) and (C) are both false. The wavelength is longer and the amplitude is smaller in deep water.

(C) is false. The amplitude increases near the shore, so it is smaller in deep water.

(A) and (C) are false. Only (B) is true.

Conclusion

Only (B) is true. (A) and (C) are false.

The answer is (2).

The facts we have are about the wave reaching the shore. For deep water, turn each one around.

Near the shore the wave is slower, shorter and taller. In deep water it is faster, longer and lower.

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