Waves and Sound
What this domain tests
Waves and Sound tests the wave equation, superposition, stationary waves, beats, pipes and strings, and the Doppler effect.
Core rules
- v = fλ; for a stretched string v = √(T/μ).
- Progressive wave y = A sin(ωt − kx); k = 2π/λ.
- Stationary waves have nodes and antinodes; adjacent nodes are λ/2 apart.
- Open pipe: all harmonics, f_n = nv/2L. Closed pipe: odd harmonics only, f_n = (2n−1)v/4L.
- Beats: f_beat = |f1 − f2|.
- Doppler effect: apparent frequency changes when source or observer moves; the sign depends on approach or recession.
Worked example
A closed organ pipe is 0.50 m long and the speed of sound is 340 m s⁻¹. Fundamental frequency f1 = v/4L = 340/(4 × 0.50) = 170 Hz. The next allowed harmonic is the third: 3 × 170 = 510 Hz. The second harmonic at 340 Hz is absent because a closed pipe supports only odd harmonics.
Traps
- Using the open-pipe formula for a closed pipe, especially in the fundamental.
- Confusing wave speed with particle speed; particles oscillate while the wave pattern travels.
- Getting the Doppler sign wrong when the source approaches.
- Forgetting that beats require frequencies close enough to be heard separately.