P6 Waves

A wave transfers energy from one place to another without transferring the material (matter) it travels through.

In a transverse wave, the particles of the medium oscillate (vibrate) at right angles (perpendicular) to the direction the wave travels and the energy is transferred. They have crests (peaks) and troughs.

In a longitudinal wave, the oscillations are parallel to (along) the direction the wave travels. They have compressions (where particles are closer together, causing higher pressure) and rarefactions (where particles are further apart, causing lower pressure).

Sound needs a medium to travel through and cannot travel through a vacuum. Electromagnetic waves do not need a medium.

A transverse wave (top) oscillates perpendicularly to the direction of wave travel. A longitudinal wave (bottom) has compressions and rarefactions oscillating parallel to the direction of wave travel.

Give two examples of transverse waves and one example of a longitudinal wave.

Transverse waves: ripples on the surface of water, and all electromagnetic waves (such as light or radio waves).

Longitudinal waves: sound travelling through air.

Remember that the material itself does not travel with the wave. For example, a cork floating on a pond bobs up and down as ripples pass, but it does not travel along with them.

A common mistake is thinking sound is a transverse wave. Sound is longitudinal. Similarly, never describe compressions as regions where particles are spread apart.

Waves transfer energy without transferring matter.

Amplitude is the maximum displacement from the undisturbed (rest) position.

Wavelength (λ) is the distance from one point to the same point on the next wave. Unit: metres (m).

Frequency (f) is the number of waves passing a point each second. Unit: hertz (Hz).

Period (T) is the time for one complete wave to pass. Unit: seconds (s).

Wave speed (v) is the speed at which energy is transferred.

Period = 1 ÷ frequency: T = 1 ÷ f

Wave speed = frequency × wavelength: v = f λ (v in m/s, f in Hz, λ in m)

You can measure the speed of sound using wave speed = distance ÷ time. Two people stand a measured distance apart. One bangs two blocks together. The other starts a stopwatch on seeing the hit and stops it on hearing the sound. Speed = distance ÷ time. Use a large distance and repeat to reduce the effect of reaction time.

Amplitude is measured from the rest position to a crest. Wavelength is measured from one crest to the next crest.

A wave has a frequency of 1.5 kHz and a wavelength of 0.22 m. What is its wave speed?

Convert frequency: 1.5 kHz = 1500 Hz.

v = f λ = 1500 × 0.22 = 330 m/s

Amplitude is measured from the rest position to a crest, NOT crest to trough.

Higher frequency does not mean a faster wave in the same medium. A higher frequency means a shorter wavelength.

Convert units before calculating: kHz to Hz (× 1000) and cm to m (÷ 100).

Electromagnetic waves are transverse waves that transfer energy from a source to an absorber. For example, a microwave oven transfers energy to food, and the Sun transfers energy to your skin by infrared.

They form a continuous spectrum. All electromagnetic waves travel perfectly through a vacuum (space) at exactly the same speed: 3.0 × 10⁸ m/s. They do not need a medium to travel.

The electromagnetic spectrum in order. Our eyes can only detect visible light, which is a very small part of the whole spectrum. Red light has the longest wavelength of visible light; violet has the shortest.

You can calculate wave speed, frequency or wavelength using the wave equation: v = fλ, so wave speed = frequency × wavelength.

Because the wave speed v is constant (3.0 × 10⁸ m/s), if the wavelength gets longer, the frequency must get lower. The energy carried by an electromagnetic wave increases with its frequency.

Red light has a wavelength of 7.0 × 10⁻⁷ m. The speed of electromagnetic waves is 3.0 × 10⁸ m/s. What is its frequency?

Rearrange the wave equation: frequency = wave speed ÷ wavelength.

f = v ÷ λ = 3.0 × 10⁸ ÷ 7.0 × 10⁻⁷

f = 4.3 × 10¹⁴ Hz

You must remember the exact order of the groups, starting with radio waves (longest wavelength, lowest frequency) and ending with gamma rays (shortest wavelength, highest frequency).

Do not confuse radio waves with sound waves. Radio waves are part of the electromagnetic spectrum, they are transverse, and they can travel through a vacuum. Sound waves are longitudinal and need a medium.

Always convert prefixes like MHz or km into standard units (Hz, m) before calculating.

When a wave crosses a boundary between two different materials at an angle, it changes direction. This is called refraction.

Ray diagrams show this happening. A ray is a straight line with an arrow. The normal is a dashed line drawn at 90° to the boundary where the ray meets it. All angles are measured between the ray and the normal.

When entering a denser medium (like going from air into glass or water), the ray bends towards the normal. The angle of refraction is smaller than the angle of incidence.

When leaving a denser medium (like going from glass or water into air), the ray bends away from the normal. The angle of refraction is larger than the angle of incidence.

A ray travelling exactly along the normal (angle of incidence = 0°) passes straight through without bending.

A light ray passing through a parallel-sided glass block. The emergent ray is parallel to the incident ray, but shifted sideways.

A ray of light in air hits the top face of a rectangular glass block at 35° to the normal and leaves through the parallel bottom face. Describe its path.

At the top face the light enters a denser medium, so it bends towards the normal: the angle of refraction is less than 35°.

At the bottom face it leaves the glass, so it bends away from the normal and comes out at 35° to the normal.

The emergent ray is parallel to the incident ray, shifted sideways.

Always measure angles from the normal, never from the surface of the block.

A pencil in water looks bent, and a pool looks shallower than it really is, because light bends away from the normal as it leaves the water.

Electromagnetic waves can be given out or absorbed when changes happen inside atoms. For example, when electrons change energy level. Gamma rays are different: they are given out by changes in the nucleus of an atom.

Ultraviolet waves, X-rays and gamma rays can harm body tissue. How harmful they are depends on the type of radiation and the size of the dose.

Radiation dose is a measure of the risk of harm resulting from an exposure of the body to the radiation. It is measured in sieverts (Sv). There are 1000 millisieverts (mSv) in 1 sievert.

Ultraviolet (UV) radiation makes the skin age early and increases the risk of skin cancer. Protection includes sunscreen, clothing, sunglasses, and limiting time in strong sun.

X-rays and gamma rays are ionising radiation. They can damage DNA and cause gene mutations, which may lead to cancer. Protection includes lead screens, film badges, and limiting the number of scans.

A patient has two CT scans of the chest in one year, each giving a dose of about 6.6 mSv. The average UK dose from background radiation is about 2.7 mSv per year. What is the total scan dose in sieverts, and how does it compare with the background dose?

Total scan dose = 2 × 6.6 = 13.2 mSv.

In sieverts: 13.2 ÷ 1000 = 0.0132 Sv.

Compare: 13.2 ÷ 2.7 ≈ 4.9, so the scans give almost five times the yearly background dose. This extra risk is weighed against the benefit of the diagnosis.

Do not confuse the source of gamma rays (the nucleus) with the source of other EM waves (the electrons).

A higher dose in sieverts means a higher risk of harm, not a lower risk.

Not all electromagnetic waves are equally dangerous; radio waves do not cause cancer like X-rays do.

Electromagnetic waves have many practical applications depending on their wavelength.

Radio waves are used for broadcasting television and radio.

Microwaves are used for communicating with satellites and for cooking food in a microwave oven.

Infrared is used for electric heaters, cooking food, infrared cameras and television remote controls.

Visible light is used for fibre optic communications (sending signals as pulses of light along glass fibres).

Ultraviolet is used for energy-efficient lamps, sun tanning and security marking pens.

X-rays and gamma rays are both used for medical imaging and treatment. X-rays can image broken bones, while gamma rays are used as tracers.

A hospital uses a beam of electromagnetic waves to kill cancer cells in a tumour. Name one type of wave that could be used, and say how its frequency compares with ultraviolet.

Gamma rays (or X-rays) are used for medical treatment such as killing cancer cells.

The order of the spectrum is radio, microwave, infrared, visible, ultraviolet, X-ray, gamma, with frequency increasing along it.

So gamma rays (and X-rays) have a higher frequency than ultraviolet.

Do not confuse television broadcasting (radio waves from a ground mast) with satellite television (microwaves passing through the atmosphere).

Fibre optic broadband uses visible light, not radio waves or microwaves.

Electric heaters use infrared, not ultraviolet. Ultraviolet is for energy-efficient lamps and sunbeds.

Electromagnetic waves transfer energy. How a material absorbs, transmits, or reflects them depends on their wavelength. For instance, glass transmits visible light but absorbs ultraviolet, and the atmosphere reflects some radio signals.

Radio waves can be produced by alternating currents in electrical circuits. When absorbed by a receiving aerial, they induce an alternating current with the same frequency.

When a wave enters a slower material at an angle, the part of the wave front that hits the boundary first slows down first. This causes the wave to bend towards the normal.

When a wave changes speed at a boundary, its frequency stays the same. The wave equation v = fλ (speed = frequency × wavelength) shows that if speed decreases, wavelength must also become shorter. This is why wave fronts are drawn closer together in a slower medium.

Light with a wavelength of 4.8 × 10⁻⁷ m in air passes into water. Its speed falls from 3.0 × 10⁸ m/s to 2.25 × 10⁸ m/s. What is its wavelength in the water?

The frequency does not change at the boundary. Find it from the values in air: f = v ÷ λ = 3.0 × 10⁸ ÷ (4.8 × 10⁻⁷) = 6.25 × 10¹⁴ Hz.

New wavelength: λ = v ÷ f = 2.25 × 10⁸ ÷ (6.25 × 10¹⁴) = 3.6 × 10⁻⁷ m. The wavelength is shorter because the light is slower.

Different waves suit different uses. Microwaves pass through the atmosphere to satellites, while X-rays pass through soft tissue but are absorbed by denser bone to form an image.

The frequency of a wave never changes when crossing a boundary, only the speed and wavelength change.

Measure wave properties using a ripple tank for water waves or a vibration generator for waves on a string.

Ripple tank: Set up a shallow tray of water with a vibrating bar driven by a motor. A lamp above casts wave shadows onto paper below.

Measure across 10 waves with a ruler and divide by 10 for wavelength. Count waves passing a point in 10 seconds and divide by 10 for frequency.

Stretched string: Tie a string to a vibration generator, pass it over a pulley, and hang a mass to keep it taut.

Adjust the frequency to see a clear stationary wave pattern. Measure across several loops. One loop is half a wavelength.

Variables (string): Independent = frequency. Dependent = wavelength. Control = tension (use the same hanging mass) and the same string.

Equation: v = f × λ (wave speed = frequency × wavelength). Speed in m/s, frequency in Hz, wavelength in m.

Hazards: The hanging mass could fall, so keep feet clear. Water could spill near electrical equipment, so wipe it up. A flashing stroboscope can trigger epilepsy.

A ripple tank is used to measure the wavelength and frequency of water waves.

Always measure across several waves or loops and divide by the number of waves to reduce the effect of random measurement errors.

If water waves move too fast to count, use a stroboscope to "freeze" the pattern.

Remember one loop on a string is only half a wavelength.

This practical finds out how the type of surface affects how much infrared radiation it emits or absorbs.

Emission method

1. Place a Leslie cube on a heatproof mat. Its four vertical faces are matt black, shiny black, matt white and shiny silver.

2. Fill the cube with very hot water.

3. Place an infrared detector a set distance (e.g. 10 cm) from one face and record the reading.

4. Move the detector to the same distance from each other face in turn and record each reading.

Absorption method: place a matt black plate and a shiny silver plate the same distance from a heater, with a drawing pin stuck to the back of each with wax. The pin on the matt black plate falls first.

Variables

Independent: the type of surface on the cube face.

Dependent: the amount of infrared radiation emitted.

Control: the distance from the face to the detector, water temperature, and surface area.

Apparatus

An infrared detector has a high resolution and a fast response. A thermometer responds much more slowly.

Hazards: The water and the Leslie cube get very hot and can scald. Stand the cube on a heatproof mat and do not touch it.

The detector measures the infrared emitted by the shiny silver face. It is then moved to the same distance from each of the other faces.

Conclusion: Dark, matt surfaces are the best emitters and best absorbers of infrared radiation. Light, shiny surfaces are the poorest emitters and absorbers (they reflect it instead).

Errors: The hot water inside cools down during the experiment. This means a later face might give a falsely low reading. Take all readings quickly to improve accuracy.

Processing: repeat each reading, discard any anomaly and compare the mean for each face.