The complete lecture — every idea comes alive in the live panel on the right as you read, drawn from real life: a stone dropped in a Clifton pond, a shaken rope, a singing sitar, an ambulance racing past. Press ▶ and let the narration carry you through; or scroll, and the dark stage keeps pace.
A wave is a travelling disturbance that carries energy and momentum through a medium without any net transport of the medium itself. Drop a stone into a still pond at Clifton: rings of ripples race outward across the surface, yet a leaf floating nearby only bobs up and down in place. The energy crosses the pond; the water stays.
Each particle of the medium performs simple harmonic motion about its own mean position (in metres of displacement); only the pattern moves on. The amplitude A is the greatest displacement from the mean, and the energy a wave carries is proportional to A².
Shake one end of a rope up and down: humps and dips (crests and troughs) run along the rope while each rope particle moves only up and down — this is a transverse wave, particle motion perpendicular to the wave. Now push and pull a Slinky along its own length: bunched coils (compressions) and stretched coils (rarefactions) chase each other along — a longitudinal wave, particle motion parallel to the wave.
| Transverse | Longitudinal | |
|---|---|---|
| Particle motion | ⊥ to wave | ∥ to wave |
| Pattern | crests & troughs | compressions & rarefactions |
| Examples | rope, sitar string, water surface, light | sound in air, Slinky push-pulse |
A struck sitar string pushes the surrounding air into a compression, then leaves a rarefaction as it swings back; these pressure pulses travel out as a longitudinal sound wave. Sound needs a medium — pump the air from a bell jar and the ringing bell falls silent. Speed of sound ≈ 331 + 0.61T m/s (T in °C), about 343 m/s at 20 °C; solids > liquids > gases.
Three things describe any sound: loudness follows amplitude (intensity ∝ A²), pitch follows frequency, and quality (timbre) follows the waveform — the mix of overtones that makes a flute and a sitar on the same note sound different. Loudness is measured on the logarithmic decibel (dB) scale: 0 dB threshold, ~60 dB talk, ~120 dB pain.
Doppler effect: relative motion between source and observer changes the apparent frequency. An ambulance racing along Sharea Faisal bunches its wavefronts as it approaches — shorter λ, higher pitch — and stretches them as it recedes — longer λ, lower pitch. The siren itself never changes; only the spacing of the wavefronts reaching your ear does.
Principle of superposition: where waves overlap, the resultant displacement is the sum of the individual displacements; the waves then pass on unchanged. Drop two stones in the pond and their rings cross — along some lines crests pile on crests, along others crest fills trough.
Two loudspeakers on one signal make loud-and-quiet bands across a room; two ripple-tank dippers draw the same pattern in water. Noise-cancelling headphones are deliberate destructive interference — proof that sound is a wave, because particles could never cancel.
Sound two notes of slightly different frequencies together and they slide in and out of phase: in phase → loud, out of phase → quiet. This periodic throb of loudness is a beat.
Tuning by beats: a sitar or tabla player sounds the instrument against a harmonium note or tuning fork. Beats heard → out of tune; the player tightens or loosens the string until the throbbing slows and vanishes — zero beats means perfectly in tune. Piano tuners do exactly the same.
Two identical waves travelling in opposite directions (a wave and its reflection) superpose into a stationary wave: the pattern stops travelling and a plucked guitar or sitar string vibrates in fixed loops.
Resonance & the tube practical: drive a body at its natural frequency and it responds with large amplitude. A struck fork (known f) hums over a tube while the water falls; the air column booms at L₁ ≈ λ/4 and L₂ ≈ 3λ/4, giving λ = 2(L₂ − L₁) and v = 2f(L₂ − L₁).
Every idea in this chapter is one sentence: a wave moves energy through a medium while the matter stays put — from the pond's ripples to the air carrying a qawwali.