Playbook
Superposition of Waves
123 q - 3.00/paper - 20% HARD. Reading a wave equation is the cheap entry at 9%; beats and the sonometer carry the HARD at 41%. Prepare it with Sound.
- Questions in the bank
- 123
- q/paper (2024–25 papers)
- 3.00
- Tagged HARD
- 20%
- Subtopics
- 5
Strand: Cornerstone
When you’ll see it
A wave equation y = A sin(ωt − kx), a string fixed at both ends, a pipe open or closed, two sources a few hertz apart, or a sonometer wire.
How this chapter is tested
123 q at 3.00 a paper, 20% HARD. The cheapest page is reading a wave equation: Progressive Wave, Wave Equation, and Velocity is 34 questions at 9% HARD, and every one comes down to picking ω and k out of the equation and using v = ω/k.
Stationary Waves and Vibrating Strings is the biggest page (36 q, 19%): nodes, antinodes, and the harmonics of a string, fₙ = nv/2L with v = √(T/μ). Pipes follow the same logic with one twist — a closed pipe has only odd harmonics.
The expensive page is Beats and Sonometer, 22 questions at 41% HARD: a tuning fork and a wire or a pipe a few hertz apart, and the question is which way the beat frequency moves when the wire is loaded or the fork waxed. Sound repeats pipes, beats and Doppler almost exactly, so prepare the two chapters together.
The sub-skills
The distinct skills inside the chapter, in the order to learn them.
Reading the wave equation
y = A sin(ωt − kx): v = ω/k, λ = 2π/k, f = ω/2π. The sign between the terms gives the direction of travel.
Strings
fₙ = (n/2L)√(T/μ). All harmonics present; μ is mass per unit LENGTH, not the string's mass.
Pipes and end correction
Open: fₙ = nv/2L, all harmonics. Closed: fₙ = nv/4L, odd n only. End correction adds 0.6r per open end.
Beats
Beat frequency = |f₁ − f₂|. Loading a fork lowers its frequency; decide the sign from whether the beats rise or fall.
Traps to expect
Distractor shapes this chapter reuses. The Traps page covers the patterns that cut across chapters.
Giving a closed pipe even harmonics
A pipe closed at one end has only odd harmonics, so its first overtone is the THIRD harmonic. Treating it as the second gives an option.
Using the string's mass for μ
v = √(T/μ) needs mass per unit length. A 10 g string of 0.5 m has μ = 0.02 kg/m, not 0.01 kg.
Learn it before you drill it
This chapter has full teaching notes — foundations, worked examples, self-checks and a per-subtopic mastery checkpoint. Read the notes once, then drill subtopic by subtopic below.
Superposition of Waves notesDrill every superposition of waves question
123 questions from the bank, scoped to 5 bundled subtopics.
Drill one subtopic at a time
The 5 subtopics this playbook covers, in catalog order.
Related playbooks
Often paired with this one — the technique, the trap or the taxonomy overlaps. Drill these next.