DSE Physics: Waves — Tutor Lesson Plan (v = f x lambda, refraction, standing waves)

2026-10-28

Tutor lesson-prep guides · Secondary physics

Students recite v = f x lambda but read wavelength off a graph as the distance from crest to trough. This lesson makes graph reading a physical routine: fix the scale, then count crest to crest.

Objectives — the student can read wavelength and amplitude from a displacement graph, apply the wave equation, find a refracted angle, and relate nodes to harmonic number.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Unit conversion	How many centimetres in 3.4 m?	340 cm
Sine values	What is sin 30 degrees?	0.5
Period	The period of a 50 Hz wave	0.02 s

02 Lesson flow (60 minutes)

Time	Stage	Tutor does	Student does
0-8 min	The graph	What one square means; counting wavelength	Mark one full wave
8-22 min	Wave equation	Solve v, f and lambda in turn	Get 170 m/s
22-36 min	Refraction	Snell law; dense against less dense	Get 19.5 degrees
36-50 min	Standing waves	Nodes, antinodes, fundamental and harmonics	Draw the third harmonic
50-56 min	Answer format	Formula, substitution, units, figures	Rewrite one answer
56-60 min	Exit check	Three questions marked	Finish alone

03 Teaching script (read it out)

Scene 1: Graph first: what does one square mean

The horizontal axis is distance and the vertical axis is displacement. Amplitude is the height from the centre line to a crest; wavelength is crest to crest.
The common error is treating crest to trough as a wavelength, so count it out loud with them.

Student states the wavelength in squares and the value of one square.

Scene 2: Refraction: into a denser medium the ray bends to the normal

n = sin i / sin r. From air into glass with n = 1.5 at 30 degrees, sin r = 0.5 / 1.5 = 0.3333, so r is about 19.5 degrees.
Frequency is set by the source and does not change; speed and wavelength both fall.

Note: angles are always measured from the normal, never from the surface.

Scene 3: Standing waves: nodes tell you the harmonic

A string fixed at both ends fits n half-waves, so lambda = 2L / n and f = nv / (2L).
With v = 180 m/s and L = 1.5 m the fundamental is 60 Hz and the third harmonic is 180 Hz. Nodes number n + 1.

Student calculates the fifth harmonic on the same string (300 Hz).

04 Question types and worked steps

Type	Example	Steps	Answer
Graph reading	wavelength from a graph	Fix the scale, count crest to crest	lambda = 3.4 m
Calculation	v = f x lambda	50 x 3.4	170 m/s
Refraction	n = sin i / sin r	sin r = sin 30 / 1.5	19.5 degrees
Standing wave	f = nv / (2L)	n = 3: 3 x 180 / 3.0	180 Hz

Sanity check (teach this): Refraction into a denser medium always gives r smaller than i. If r comes out larger, n is upside down or the angle was measured from the surface.

05 Independent practice (3 questions)

Question	Answer	What to watch
v = f x lambda with 50 Hz and 3.4 m	170 m/s	Are the units written
Air to glass, i = 30 degrees, n = 1.5	about 19.5 degrees	Measured from the normal
v = 180 m/s, L = 1.5 m, fundamental	60 Hz	Was 2L used

06 Common mistakes and what to say

Mistake	Student writes	Say this
Crest to trough called a wavelength	lambda halved	Crest to crest, or trough to trough, is one wave.
Angle measured from the surface	r written as 70.5 degrees	All angles are measured from the normal.
Frequency changed by refraction	f also falls	The source sets the frequency; speed and wavelength change.
Nodes counted as harmonics	third harmonic with 3 nodes	Nodes are n + 1.

07 Homework (paper, section and question numbers)

DSE Physics practice paper (wave and heat calculations) — Section A (wavelength, sound speed)
Secondary physics chapter index — All chapters

08 Exit check (last 5 minutes)

Question	Answer	Decision
Speed with 50 Hz and 3.4 m	170 m/s	All three right: move to sound
Refracted angle, 30 degrees into n = 1.5	about 19.5 degrees	One wrong: re-teach refraction
Third harmonic, v = 180, L = 1.5	180 Hz	Two wrong: repeat scene 3

09 Tutor FAQ

Memorise sine values?

The common 30, 45 and 60 degree values; others are given or come from a calculator.

Displacement graph or oscillation graph?

Distance on the axis is a wave profile; time on the axis is an oscillation.

Are standing waves examined?

Yes, usually only fundamental and harmonics with lambda = 2L / n.

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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.