Revise Wave model for IB Physics (C.2)

Every wave carries energy through a repeating oscillation, but waves split into two families according to the direction of that oscillation. In a transverse wave the particles oscillate at right angles to the direction the wave travels — a wave sent along a rope, ripples on water, and every electromagnetic wave including light. In a longitudinal wave the particles oscillate back and forth along the direction of travel, squeezing the medium into regions of high density (compressions) and low density (rarefactions). Sound in air is the standard longitudinal wave. In both families the medium itself does not travel with the wave: each particle simply oscillates about its own fixed rest position while the disturbance moves on.

To describe a wave quantitatively we need five terms. The amplitude ($A$) is the maximum displacement of a particle from its rest position, and it sets how much energy the wave carries. The wavelength ($\lambda$) is the shortest distance between two points oscillating in phase — crest to crest, or compression to compression — measured in metres. The period ($T$) is the time for one complete oscillation, measured in seconds. The frequency ($f$) is the number of complete oscillations per second, measured in hertz (Hz). Finally the wave speed ($v$) is the distance the disturbance travels each second, in m s⁻¹.

Frequency and period describe the same repetition — one in cycles-per-second, the other in seconds-per-cycle — so they are reciprocals of each other. This gives the first relationship. The second, the wave equation, follows from a simple idea: in one period the wave advances exactly one wavelength, so its speed is one wavelength divided by one period, which rearranges to speed = frequency × wavelength.

T = \dfrac{1}{f} \qquad\qquad v = f\lambda

Here $v$ is the wave speed in m s⁻¹, $f$ is the frequency in Hz, $\lambda$ is the wavelength in m, and $T$ is the period in s. Because $v = f\lambda$ links three quantities, knowing any two immediately gives the third. Keep firmly in mind which quantity is controlled by what: the frequency is fixed by the source, while the speed is fixed by the medium — so when a wave crosses into a new medium it is the wavelength that must change.

There are two complementary ways to draw a wave as it spreads out. A wavefront is a line (or surface) joining points that are all in phase — for instance the line running along the top of one crest. Successive wavefronts are therefore spaced exactly one wavelength apart. A ray is an arrow drawn at right angles to the wavefronts, pointing in the direction the wave travels — that is, the direction of energy transfer. A wave spreading out from a point source has circular wavefronts; a wave far from its source, or a beam, has straight (plane) wavefronts. Rays and wavefronts always cross at 90°, so a diagram with either one implies the other.

The single most tested — and most confused — skill in this topic is reading a wave off a graph, because a displacement–distance graph and a displacement–time graph look identical yet mean different things. A displacement–DISTANCE graph is a snapshot: it freezes the whole wave at one instant and plots the displacement of every particle along the wave. The horizontal length of one full cycle is therefore the WAVELENGTH. A displacement–TIME graph is a movie of a single particle: it plots how that one particle's displacement changes as time passes. The horizontal length of one full cycle is therefore the PERIOD. Both graphs are sine curves and both show the amplitude on the vertical axis — so always read the horizontal axis label first to know whether you are getting a wavelength or a period.

Visible light is one small band of a much larger family of transverse waves called the electromagnetic (EM) spectrum. In order of increasing frequency (and therefore decreasing wavelength) the regions are: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays. Although they interact with matter in wildly different ways — radio waves pass through walls while gamma rays are ionising — they share one defining property: in a vacuum every one of them travels at the same speed, $c = 3.0 \times 10^8$ m s⁻¹. Because $c = f\lambda$ is fixed in a vacuum, the higher-frequency regions automatically have the shorter wavelengths.

A mechanical wave is a disturbance passed from particle to particle through a material, so it cannot exist without that material. Sound, water waves, waves on a string and seismic waves are all mechanical — remove the medium and the wave disappears, which is why a bell ringing inside a jar goes silent as the air is pumped out and why space is soundless. Electromagnetic waves are the exception: they are oscillations of electric and magnetic fields that carry themselves along, needing no particles at all, so light from the Sun crosses the vacuum of space to reach us. This is the fundamental practical divide between the two categories of wave.

In Paper 2 the marks are analytic: each is tied to a specific line of working — a method mark (M) or an answer mark (A) — and error-carried-forward (ECF) means a wrong number early on does not have to cost you the marks that follow. But that protection only exists if your method is written down. The question below deliberately mixes a calculation with a 'state and explain' part, because the explaining marks are earned by distinct physics statements, not by the number.

The wave model you have built here is the foundation for everything in wave behaviour that follows. The wave equation reappears whenever a wave changes medium — the physics of refraction is simply $v = f\lambda$ with the frequency held constant. Wavefronts and rays become the tools for describing reflection, refraction and diffraction, and the amplitude you learned to read off a graph is what determines intensity when waves superpose and interfere. Master the habit — identify the wave type, read the right graph for the right quantity, rearrange before you substitute, and keep frequency and medium in their proper roles — and the rest of the topic becomes variations on a model you already own.