General Properties of Waves

Transverse wave. The oscillation is PERPENDICULAR to the direction the wave travels. The named examples in the syllabus are electromagnetic radiation (light, radio, etc.), water waves and seismic S-waves (secondary waves) — all modelled as transverse.

Longitudinal wave. The oscillation is PARALLEL to the direction of travel — particles squeeze together (compressions) and stretch apart (rarefactions). The named examples are sound waves and seismic P-waves (primary waves) — both modelled as longitudinal.

Seismic waves are produced by earthquakes and travel through the Earth. Remember: P for Parallel vibration (longitudinal) and S for Sideways vibration (transverse).

Wavefronts. A wavefront is a line (or surface) joining all the points of a wave that are vibrating exactly in step — for example, a line joining a row of crests. Adjacent wavefronts are one wavelength apart. Drawing waves as a set of parallel wavefronts is a convenient way to show reflection, refraction and diffraction.

Both types share the features wavefront, wavelength, frequency, crest (peak), trough, amplitude and wave speed.

Drawing.

• Transverse: a sine curve with crests (peaks) and troughs.
• Longitudinal: a series of compressions (close particles) and rarefactions (spread particles).

Energy not matter. Waves transfer ENERGY without transferring matter. A floating cork bobs up and down as water waves pass — it doesn't travel with the wave.

Wavelength $\lambda$: distance from one peak to the next (or one compression to the next). Units: $\text{m}$.

Frequency $f$: number of complete waves per second. Units: hertz ($\text{Hz}$).

Period $T$: time for one complete oscillation. $T = 1/f$. Units: $\text{s}$.

Amplitude $A$: maximum displacement from rest position. Determines how much energy the wave carries.

Wave speed $v$: how fast the wave travels. $\text{m/s}$.

Wave equation. $v = f\lambda.$

Worked. A water wave has wavelength $0.5\,\text{m}$ and frequency $2\,\text{Hz}$. Find speed.

• $v = 2 \times 0.5 = 1\,\text{m/s}$.

Worked. Sound in air at $340\,\text{m/s}$, frequency $500\,\text{Hz}$. Find wavelength.

• $\lambda = v/f = 340/500 = 0.68\,\text{m}$.

Tip. Always rearrange the equation to isolate the unknown — don't try to memorise three variants.

Reflection. When a wave bounces off a surface.

• Law of reflection: angle of incidence = angle of reflection (both measured from the NORMAL, not the surface).

Refraction. When a wave crosses into a different medium, its speed changes — and if it hits at an angle, its direction bends.

• Going into a denser/slower medium → wave SLOWS down → bends TOWARD the normal.
• Going into a less dense/faster medium → SPEEDS up → bends AWAY from normal.
• Wavelength changes; frequency stays the same.

Worked qualitative. Light entering glass slows down → bends toward normal. Exiting back into air → speeds up → bends away from normal.

Tip. Always draw the normal (perpendicular) line at the boundary first. Both angles are measured from it.

Diffraction. Waves bend or spread out when they pass through a gap or round an obstacle.

Amount of diffraction depends on the size of the gap relative to the wavelength:

• Gap MUCH larger than $\lambda$: little diffraction.
• Gap $\approx \lambda$: maximum diffraction.
• Gap smaller than $\lambda$: still spreads, but less wave gets through.

Why we hear round corners. Sound has long wavelengths (cm-m), so it diffracts well around doorways, walls, etc. Light has very short wavelengths (nm), so it doesn't diffract noticeably round corners — that's why you can't see round them.

Worked qualitative. A ripple tank with parallel plane waves hits a barrier with a small gap — circular waves spread out from the gap on the other side. With a wide gap, the waves continue mostly straight with only slight curving at the edges.