Physics

Waves

6,008 words, 10 sections

This chapter is the physics of anything that travels as a disturbance rather than as a lump of matter: ripples in a rope, pulses in a spring, sound in air, light in vacuum. The MDCAT examines it heavily, with 507 distinct questions across 95 official papers between 2000 and 2026, set by every board that sits the paper. That makes waves the single largest block of physics in the bank, and a mean item difficulty of 1.67 on the bank scale means most of those questions are meant to be answered rather than endured. A student who has mastered this material can classify any wave, move fluently between wavelength, frequency and speed, work out stationary waves on strings and in pipes, and handle the Doppler effect numerically, which together cover the great majority of the marks.

Wave motion begins with a simple observation. Shake one end of a stretched rope or strike a spring, and the disturbance runs to the far end while every small piece of the rope stays close to where it started. The particles of the medium oscillate about fixed mean positions, and what advances is the pattern, not the matter. For this to happen the medium must be elastic: a displaced particle has to feel a restoring force pulling it back, otherwise the disturbance dies where it began. That single condition, elasticity, is why wave motion needs a medium at all.

That gives the first division. Mechanical waves require a material medium, because they propagate by making neighbouring particles push and pull on each other. Electromagnetic waves do not: they propagate through the changing electric and magnetic fields themselves and cross empty space without difficulty. Sound, water ripples, earthquake waves and waves on a spring are mechanical; light, radio, X-rays and gamma rays are electromagnetic. A progressive wave of either kind carries energy and momentum across the medium as it travels, but it carries no net matter, because each particle simply passes its disturbance to the next and settles back.

The second division concerns how the particles move relative to the direction of travel. In a transverse wave the particles oscillate at right angles (perpendicular) to the direction of propagation; a wave on a plucked string and a ripple on water are the standard examples. In a longitudinal wave the particles oscillate back and forth along the direction of propagation, which produces travelling regions of crowding and thinning called compressions and rarefactions. Sound in air is longitudinal. A compression is a region of high pressure and high density; a rarefaction is the low-pressure region between compressions. Because the oscillation direction is the whole difference, transverse waves can be polarised (their vibrations can be confined to a single plane) while longitudinal waves cannot, since there is no perpendicular plane to restrict them to.

Worked example

A student is told that a pulse is sent along a stretched spring and that a beam of light leaves a torch at the same moment. Decide, for each, whether a medium is required and whether the wave can be polarised. Reasoning: the spring pulse is mechanical, so it requires the spring; if it was made by a sideways flick, the coil oscillates perpendicular to the direction of travel, so it is transverse and can be polarised. The light requires no medium, because it is electromagnetic and crosses a vacuum; it is also transverse, so it too can be polarised. The decisive step, and the one students skip under time pressure, is that "mechanical versus electromagnetic" answers the medium question and is completely separate from "transverse versus longitudinal", which answers the polarisation question. A wave can be mechanical and transverse at once, which is exactly what the spring pulse is.

8 more sections in this chapter

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Introduction

1. Wave motion and the two great divisionsWave motion begins with a simple observation. Shake one end of a stretched rope or strike a spring, and the disturbance runs to the far end while every small pi