Waves

Explanation

• In a transverse wave, oscillations are perpendicular to the direction of energy transfer; in a longitudinal wave, oscillations are parallel to it.
• Use the direction the particles or points oscillate, not the direction the whole wave travels, to classify a wave.
• A floating marker can bob up and down while a ripple moves horizontally, showing that the disturbance and energy travel without the water moving along with the wave.
• Do not call every mechanical wave longitudinal: water-surface ripples are treated as transverse, while sound waves in air are longitudinal and contain compressions and rarefactions.

Explanation

• Amplitude is the maximum displacement from the undisturbed position; wavelength is the distance between equivalent points on adjacent waves; frequency is waves per second and period is time per wave.
• Measure several complete wavelengths or periods and divide by their number to reduce percentage uncertainty; for sound, two microphones and a measured separation can provide a travel time.
• Use $T=1/f$ and $v=f\lambda$.
• For example, a $5.0\,\text{Hz}$ wave has period $0.20\,\text{s}$.
• A common error is to use crest-to-trough distance as one wavelength; it is only half a wavelength, and amplitude must be measured from the undisturbed line rather than crest to trough.

Explanation

• At a boundary between materials, some incident wave energy may be reflected, some transmitted and some absorbed.
• For a reflection ray diagram, draw a normal perpendicular to the surface at the point of incidence and measure angles from the normal.
• The angle of incidence equals the angle of reflection.
• Energy accounting can test a boundary model: if $65\%$ is transmitted and $20\%$ reflected, the remaining $15\%$ is absorbed.
• Do not measure the angles from the surface or assume that every boundary reflects all of the incident wave.

Explanation

• Sound waves can make solids vibrate; in the ear, sound makes the eardrum and other structures vibrate, producing the sensation of sound.
• Trace a conversion by naming the incoming wave, the vibrating solid and any outgoing wave or electrical signal.
• Normal human hearing extends from about $20\,\text{Hz}$ to $20\,\text{kHz}$, so a $25\,\text{kHz}$ vibration is above the usual audible range.
• Do not assume that every vibrating system responds equally at all frequencies: conversion between sound and solid vibration works only over a limited frequency range.

Explanation

• Ultrasound is sound above $20\,\text{kHz}$; partial reflections at boundaries and their return times allow hidden interfaces to be located.
• For echo measurements use the total out-and-back distance, so a boundary distance is $d=vt/2$.
• P-waves are longitudinal and travel through solids and liquids, whereas transverse S-waves do not travel through liquids; their paths provide evidence about Earth's internal structure.
• A common error is to omit the factor of $2$ in echo sounding or to claim that an absent S-wave proves there are no waves rather than indicating a liquid region along its path.

Explanation

• Electromagnetic waves are transverse waves that transfer energy from a source to an absorber and form one continuous spectrum.
• Order the spectrum from long wavelength and low frequency to short wavelength and high frequency: radio, microwave, infrared, visible, ultraviolet, X-ray, gamma.
• All electromagnetic waves travel at the same speed in a vacuum, about $3.00\times10^8\,\text{m s}^{-1}$; for example, $f=5.0\times10^{10}\,\text{Hz}$ gives $\lambda=6.0\times10^{-3}\,\text{m}$.
• Do not say that higher-frequency electromagnetic waves travel faster in a vacuum; frequency and wavelength change across the spectrum, but the vacuum speed is the same.

Explanation

• Construct a refraction ray diagram using a normal at the boundary.
• Higher only: the amounts absorbed, transmitted, reflected or refracted depend on the material and wavelength.
• To compare infrared emission or absorption by surfaces, keep area, temperature, distance and detector geometry fixed, repeat readings and change only the surface finish.
• Higher only: on crossing into a slower medium, frequency stays constant, so wavelength decreases; closer wavefronts on the slower side show the speed change that causes refraction.
• Higher only: do not say refraction is caused by a frequency change; speed and wavelength change at the boundary, while frequency is fixed by the source.

Explanation

• Higher only: oscillations in electrical circuits can produce radio waves, and absorbed radio waves can induce an alternating current of the same frequency in a receiving circuit.
• Use dose data by converting units consistently: $1000\,\text{mSv}=1\,\text{Sv}$, then compare total doses rather than single exposures.
• Electromagnetic waves can be emitted or absorbed when atoms or nuclei change; gamma rays specifically originate from changes in an atomic nucleus.
• Do not treat ultraviolet, X-rays and gamma rays as equally hazardous: effects depend on radiation type and dose; ultraviolet can damage skin, while X-rays and gamma rays are ionising and can cause mutations and cancer.

Explanation

• Typical uses are radio for broadcasting; microwaves for satellite communication and cooking; infrared for heaters, cooking and thermal cameras; and visible light for fibre-optic communication.
• Higher only: explain suitability by linking the application to whether the wave is transmitted, absorbed, detected or able to penetrate the relevant material.
• Ultraviolet is used in energy-efficient lamps and tanning, while X-rays and gamma rays are used for medical imaging and treatment.
• A common error is to name a use without explaining suitability; at Higher tier, link the wave's penetration, absorption or effect on matter to the application.

Explanation

• A convex lens refracts parallel rays towards its principal focus and may form real or virtual images; a concave lens spreads rays and always forms a virtual image.
• Construct a ray diagram with at least two standard rays from the same point on the object; their intersection, or the intersection of backward extensions, locates the image.
• Magnification is $\text{image height}/\text{object height}$ and has no unit; an image $4.5\,\text{cm}$ high from an object $1.5\,\text{cm}$ high has magnification $3.0$.
• Do not attach units to magnification or use mismatched units for the two heights; a virtual image cannot be projected onto a screen.

Explanation

• Each visible colour occupies a narrow range of wavelengths and frequencies within the electromagnetic spectrum.
• A smooth surface gives specular reflection mainly in one direction; a rough surface gives diffuse reflection by scattering light, while transparent and translucent materials both transmit light but differ in image clarity.
• A colour filter absorbs some wavelength ranges and transmits others, so predict the emerging light by finding the wavelengths that both arrive and pass through the filter.
• An opaque object appears the colour it reflects most strongly; it appears white if it reflects all visible wavelengths similarly and black if it absorbs them all.
• Do not say an ordinary coloured object produces its own light.

Explanation

• Every object emits and absorbs infrared radiation, and a hotter object emits more infrared energy in a given time.
• To compare surfaces fairly, use equal areas at the same temperature and keep detector distance, angle and surroundings constant; repeat readings before comparing means.
• A perfect black body absorbs all incident radiation, reflecting and transmitting none; because a good absorber is also a good emitter, it is the best possible emitter.
• Do not confuse visible colour alone with the experimental variable: surface finish matters, and a shiny surface is generally a poorer absorber and emitter than a matt black surface.

Explanation

• All objects emit radiation, and both the intensity and wavelength distribution of the emitted radiation depend on temperature.
• Higher only: for an energy-balance question, compare the incoming radiation absorbed each second with the radiation emitted each second; equal rates mean constant temperature.
• Higher only: if a body absorbs $480\,\text{J}$ each second but emits $530\,\text{J}$ each second, it has a net energy loss of $50\,\text{J s}^{-1}$ and cools.
• Higher only: do not infer constant temperature from a constant incoming rate alone; reflection, absorption and emission all affect the balance, including for Earth's surface and atmosphere.