How is paper 4 different from the first three?

Paper 4 drills the commonest slips on wave speed, refractive index and the critical angle, with shorter items but every trap present.

Why does frequency stay the same in water?

The source sets the oscillations per second; the medium affects speed only, so the wavelength changes instead.

How does the critical angle relate to the index?

The larger the index, the smaller the critical angle, which is why diamond reaches only 24.4 degrees.

What should I do after a wrong answer?

Write down whether the slip was the formula, the units or the rounding, then redo a similar item.

S5 Physics waves paper 4: error drills and common slips

2026-11-10

Tutor Prep Guide · S5 Physics Waves and Refraction

Ten items target wave speed, refractive index, critical angles and constant frequency, each with a one-line note.

Direct answers　Items 01 to 03 cover speed and period, 04 to 06 the index and critical angle, 07 to 09 cross-medium refraction, water wave conversion and diamond reflection, 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)

FoundationA wave travels at 25 m/s with a frequency of 5 Hz. Find its wavelength.
FoundationA 250 Hz sound wave travels at 340 m/s in air. Find its wavelength.
FoundationA wave takes 0.004 s for one complete oscillation. Find its frequency.
IntermediateLight travels at 1.8 x 10^8 m/s in a medium. Find its refractive index (c = 3.0 x 10^8 m/s).
IntermediateLight enters glass (n = 1.5) from air at 45 degrees. Find the angle of refraction.
IntermediateGlass has a refractive index of 1.6. Find the critical angle from glass into air.
ChallengeLight goes from water (n = 1.33) into glass (n = 1.5) at 40 degrees. Find the angle of refraction.
ChallengeA water wave has speed 24 cm/s and wavelength 6 cm in deep water. In shallow water its speed is 20 cm/s. Find the frequency and wavelength there.
ChallengeDiamond has a refractive index of 2.42. Light hits the diamond-air boundary at 30 degrees. Find the critical angle and decide whether total internal reflection occurs.
Error redoError drill: a student writes “a 500 Hz sound wave moves from air (340 m/s) into water (1500 m/s), so the frequency becomes 500 x 1500 / 340 = 2206 Hz”. Point out the mistake and give the correct frequency and wavelength.

03　Answers and one-line notes

#	Answer	One-line note
1	Wavelength = v / f = 25 / 5 = 5 m	Wavelength is speed divided by frequency.
2	Wavelength = 340 / 250 = 1.36 m	Use 340 m/s for sound in air.
3	Frequency = 1 / 0.004 = 250 Hz	Frequency is the reciprocal of period.
4	n = 3.0 x 10^8 / 1.8 x 10^8 = 1.67	Index is the vacuum speed divided by the speed in the medium.
5	sin r = sin 45 / 1.5 = 0.4714, so r = 28.1 degrees	Find the sine first, then take the inverse sine.
6	sin C = 1 / 1.6 = 0.625, so C = 38.7 degrees	The sine of the critical angle is the ratio of the two indices.
7	sin r = 1.33 x sin 40 / 1.5 = 0.5699, so r = 34.7 degrees	Both media have an index, so the first index appears in the numerator.
8	Frequency stays 24 / 6 = 4 Hz; wavelength = 20 / 4 = 5 cm	Only speed and wavelength change; the source fixes the frequency.
9	sin C = 1 / 2.42 = 0.4132, so C = 24.4 degrees; 30 is larger, so total internal reflection occurs	Total internal reflection needs the angle to exceed the critical angle.
10	Frequency is set by the source and stays 500 Hz; wavelength = 1500 / 500 = 3 m	Changing medium alters speed and wavelength only, never frequency.

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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Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.