The complete lecture — every wave comes alive in the live panel on the right as you read. Scroll down; the dark stage keeps pace: travelling waves, compressions, beats throbbing, strings standing still in loops, and a resonance tube finding the speed of sound.
A wave is a travelling disturbance that carries energy and momentum through a medium without any net transport of the medium. At Clifton beach the swell rolls in for kilometres, yet a floating bottle only bobs in place — the water stays, the energy arrives.
Each particle of the medium does SHM about its own mean position; only the pattern moves on. In a transverse wave the particle motion is perpendicular to the wave's travel — crests and troughs, like a shaken rope or a sitar string.
In a longitudinal wave the particles oscillate parallel to the wave's direction, making travelling zones of compression (bunched) and rarefaction (spread out) — push-pull a Slinky along its length and watch the coil-bunches run.
| Transverse | Longitudinal | |
|---|---|---|
| Particle motion | ⊥ to wave | ∥ to wave |
| Pattern | crests & troughs | compressions & rarefactions |
| Examples | string, water surface, light | sound in air, Slinky push-pulse |
A vibrating tabla skin pushes air into a compression, then leaves a rarefaction as it swings back. These pressure pulses travel out as a longitudinal wave; the air itself only shivers in place.
| Characteristic | Depends on | Everyday meaning |
|---|---|---|
| Loudness | amplitude (I ∝ A²) | whisper vs shout |
| Pitch | frequency | child's voice high, man's voice low; thin sitar string vs thick |
| Quality | waveform (mix of overtones) | flute vs sitar on the same note still sound different |
Loudness is compared on the decibel scale: 0 dB threshold of hearing, ~60 dB conversation, ~120 dB pain — a rickshaw horn at your ear.
Principle of superposition: where waves overlap, the resultant displacement is the sum of the individual displacements — then the waves pass on unchanged.
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.
Two notes of slightly different frequencies slide in and out of phase: in phase → loud, out of phase → quiet. The periodic throb of loudness is a beat.
Tuning by beats: the sitar or tabla player sounds the instrument against a harmonium note or tuning fork. Beats heard → out of tune; the player tightens the string or taps the gajra until the beats slow and vanish — zero beats means perfectly tuned.
Two identical waves travelling in opposite directions (a wave and its reflection) superpose into a stationary wave: the pattern stops travelling and the string vibrates in fixed loops.
Resonance: drive a body at its natural frequency and it responds with a large amplitude — a swing pushed in time, a glass shattered by a held note.
Board practical: a tuning fork of known f hums over a vertical tube while the water level is lowered. The trapped air column (closed at the water, open at the top) booms loudly when its length fits the wave:
Doppler effect: relative motion between source and observer changes the apparent frequency. Approaching → wavefronts bunch → higher pitch; receding → stretched → lower pitch. The ambulance on Sharea Faisal screams shriller coming towards you and drops to a deeper note the instant it passes — the siren itself never changed.