Playbook
Sound
47 q - 1.04/paper - 21% HARD. Doppler and pipes — the same material as Superposition of Waves, and cheap if prepared with it.
- Questions in the bank
- 47
- q/paper (2024–25 papers)
- 1.04
- Tagged HARD
- 21%
- Subtopics
- 3
Strand: Long Tail
When you’ll see it
A source or observer moving, a pipe resonating, overtones, or two sources producing beats.
How this chapter is tested
47 q at 1.04 a paper, 21% HARD. Doppler Effect — Moving Source and Observer (19 q, 16%) and Pipes, Resonance, Overtones, and Beats (22 q, 27%) are nearly all of it.
Doppler: f' = f (v ± v_o)/(v ∓ v_s), the upper signs for approach. The same speed moves the pitch more when the SOURCE moves than when the observer does — a comparison the paper sets directly.
The pipes and beats are the same material as Superposition of Waves. Prepare the two chapters together and Sound costs little extra.
The sub-skills
The distinct skills inside the chapter, in the order to learn them.
Doppler
f' = f(v + v_o)/(v − v_s) on approach; flip both signs on recession.
Pipes and overtones
Open: all harmonics; closed: odd only. First overtone = second harmonic (open), third (closed).
Speed of sound
v ∝ √T for a gas; independent of pressure at fixed temperature.
Traps to expect
Distractor shapes this chapter reuses. The Traps page covers the patterns that cut across chapters.
Treating a moving source like a moving observer
At the same speed a moving source shifts the pitch more than a moving observer. Swapping the formulas gives the other printed option.
Pressure changing the speed of sound
At constant temperature, v does not depend on pressure. Options that scale v with P are wrong.
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.
Sound notesDrill every sound question
47 questions from the bank, scoped to 3 bundled subtopics.
Drill one subtopic at a time
The 3 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.