Does frequency change when water waves enter shallow water?

No, the frequency is unchanged while speed and wavelength both fall.

What happens beyond the critical angle?

Total internal reflection occurs and all the light returns into the first medium.

How do you get the index from a critical angle?

Use n equal to 1 divided by sin C.

Why can sine and tangent not be swapped in refraction questions?

Snell law is built on the ratio of sines, so using tangent gives a wrong angle.

S5 Physics waves paper 2: changing media and refraction calculations

2026-11-10

Tutor Prep Guide · S5 Physics Waves and Refraction

Ten items cover water waves moving into shallow water, reverse Snell law, critical angles and judging total internal reflection.

Direct answers　Items 01 to 02 cover frequency and the speed ratio of water waves, 03 to 05 Snell law, total internal reflection and reversing the index, 06 to 09 constant frequency, the water critical angle and wavelength conversion, and 10 the mistaken change of frequency.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10
Suggested time	25
Difficulty mix	Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1
Chapter	Chapter: S5 Physics Waves and Refraction
Level	S5

02　Questions (10 items)

FoundationSound of wavelength 0.5 m travels at 340 m/s. Find its frequency.
FoundationWater waves move at 20 cm per second with 4 cm wavelength in deep water and slow to 15 cm per second in shallow water. Find the new wavelength.
IntermediateLight enters glass of refractive index 1.5 from air at 40 degrees. Find the angle of refraction.
IntermediateLight inside glass of refractive index 1.5 reaches the surface at 50 degrees. Does any light leave into the air?
IntermediateA medium has a critical angle of 30 degrees. Find its refractive index.
FoundationA sound wave of wavelength 0.85 m travels at 340 m/s. Find its frequency.
ChallengeWhen a wave crosses into another medium, how do frequency, speed and wavelength change?
ChallengeWater has refractive index 1.33. Find the critical angle for light leaving water into air.
ChallengeWaves of 2 cm wavelength move at 8 cm per second in deep water and at 6 cm per second in shallow water. Find the new wavelength.
Error redoA student claims the frequency of light drops when it enters water, which bends the ray. What is correct?

03　Answers and one-line notes

#	Answer	One-line note
1	680 Hz	Frequency is speed divided by wavelength, that is 340 divided by 0.5.
2	3 cm	Frequency is unchanged, so wavelength scales with speed, 4 times 15 divided by 20.
3	about 25.4 degrees	sin theta2 is sin 40 degrees divided by 1.5, which is 0.4285.
4	No, total internal reflection occurs	The critical angle is about 41.8 degrees and 50 degrees already exceeds it.
5	2.0	Rearranging sin C equal to 1 over n gives n equal to 1 divided by sin 30 degrees.
6	400 Hz	340 divided by 0.85 is 400.
7	Frequency stays the same, speed changes and wavelength changes in the same proportion	The source fixes the frequency and the medium fixes the speed, so the wavelength adjusts to keep v equal to f lambda.
8	about 48.8 degrees	sin C is 1 divided by 1.33, which is 0.7519.
9	1.5 cm	Frequency is constant, so the wavelength is 2 times 6 divided by 8.
10	Frequency is unchanged; the ray bends because the speed drops	The frequency is fixed by the source, while the slower speed and shorter wavelength turn the ray.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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