Sec 4 Physics General Properties of Waves notes

Flick one end of a rope tied to a wall and a hump runs along it. Nothing of the rope travels — each piece simply lifts and drops in turn — but energy clearly crosses the room. That is the essence of wave motion: a wave transfers energy without transferring matter. The same story plays out in a stretched spring (a push makes a compression run along it) and in a ripple tank, where a dipping paddle sends straight ripples across shallow water while a floating cork just bobs on the spot.

A wavefront is a line joining points that are in step — for straight ripples, each crest line is a wavefront, and the wavefronts march forward like rungs of a moving ladder. Drawing wavefronts (rather than rays) is the natural language for describing reflection and, later, refraction of waves.

Two graphs describe every wave, and the only real skill is checking the axis. A displacement–distance graph snapshots the whole wave at one instant: crest spacing gives λ, peak height gives A. A displacement–time graph watches one point over time: peak-to-peak time gives T, peak height gives A. Candidates who swap them read a wavelength of 0.02 s or a period of 2 m — both instant marks lost.

In one period T the wave advances exactly one wavelength λ, so its speed is v = λ ÷ T = λ × (1/T) = λf: v = fλ. The equation holds for every wave — ripples, sound, light — because it is just distance = speed × time dressed in wave clothing.

A transverse wave oscillates across the direction of travel: flicked ropes, water ripples (surface) and all electromagnetic waves are transverse. A longitudinal wave oscillates along the travel direction, piling the medium into compressions (particles bunched, pressure high) separated by rarefactions (particles spread, pressure low). Push–pull a stretched spring and watch a compression run down it: that is longitudinal motion made visible.

Sound begins with a vibration: a drum skin pushes the air, a guitar string squeezes and releases it. The air carries the disturbance as a longitudinal wave — chains of compressions and rarefactions travelling at about 340 m/s in air (faster in water, faster still in steel). Sound needs a medium: a ringing bell in a vacuum jar falls silent as the air is pumped out, though the hammer still strikes. What reaches your ear is pressure rhythm: loudness tracks the amplitude (bigger swings, louder) and pitch tracks the frequency (more cycles per second, higher note).

Sound reflects off large hard surfaces, and the reflected sound is an echo — audible as a separate clap when the delay exceeds about a tenth of a second (roughly 17 m to the wall and back). Shorter than that, the echo merges with the original sound, making it seem louder (the reason cathedral singing sounds rich). Measuring the delay turns sound into a ruler: distance = v × t ÷ 2, the ÷ 2 because the pulse travels there and back.