Waves – GCSE Combined Science Physics

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Drop a pebble into a pond and watch what happens. A ring spreads out across the water, and that ring is a wave. If a toy duck is floating nearby, it bobs up and down as the ring passes, but it does not get carried away to the edge of the pond.

That is the big idea of this whole topic. A wave carries energy from one place to another, but it does not carry the water, the air or the rope along with it. The material just wobbles on the spot while the energy travels on, a bit like a row of dominoes where each one only falls over a short way but the knock keeps going.

Think of a Mexican wave at a football match, which is the best everyday picture of a wave. The wave runs all the way round the stadium, yet every fan stays in their own seat and only stands up and sits down. The wave is the pattern that moves, and the fans are the material it passes through, which is exactly how a wave in a rope or a pond behaves.

Waves are everywhere in your day. Sound is a wave, light is a wave, and the signal that reaches your phone is a wave. Even the heat from a toaster and the beam that cooks food in a microwave oven travel as waves, and so does the light that lets you read this screen.

By the end of this lesson you will be able to do four things. First, tell a transverse wave from a longitudinal wave and say what a wave transfers. Second, use wave speed = frequency × wavelength and describe how to measure the speed of waves. Third, describe reflection, refraction and the electromagnetic spectrum. Fourth, say what electromagnetic waves are used for and why some of them are dangerous.

Two kinds of wave

Waves come in two kinds, and the difference is the way the wave shakes the material it travels through. That shaking is called an oscillation, which means a back and forth movement around a fixed point. Every wave has an oscillation, and you can describe a wave by saying which way it points.

In a transverse wave, the oscillation is at right angles to the direction the wave travels. Picture shaking one end of a long rope up and down, so the bumps run along the rope while each bit of rope only moves up and down. Ripples on water and light are transverse waves.

In a longitudinal wave, the oscillation is parallel to the direction the wave travels, and parallel means going the same way, side by side. Picture pushing and pulling the end of a slinky spring, so squashed patches and stretched patches run along it. Sound is a longitudinal wave.

In the picture, a compression is a squashed patch where the particles are close together, and a rarefaction is a stretched patch where they are spread out. A simple memory trick is that transverse means across, and longitudinal means along. Test yourself on this with every wave you meet, such as the ripples in a washing up bowl or the sound of your own voice.

Both kinds do the same job, which is to transfer energy without carrying matter with them. Here is the evidence. A cork floating on a water ripple bobs up and down on the spot as the ripple passes, and the cork does not travel with the wave. Sound reaches your ear because air particles pass the vibration on, not because air rushes from the speaker to you. If air really did rush across the room, the papers on your desk would blow away every time someone played music.

Describing waves and the wave speed equation

To describe a wave you need five words. Learn what each one means and what unit goes with it, because mixing them up loses easy marks. Exam questions love to ask for a word and its unit, so take a moment to learn the table.

Amplitude is the biggest distance the wave rises above its rest line, which is the line the material sits on when there is no wave. A big amplitude means a lot of energy. A loud sound has a large amplitude, and a quiet sound has a small one.

Wavelength is the distance from a point on one wave to the same point on the next wave. You can measure it from crest to crest, where a crest is the top of a wave, or from trough to trough, where a trough is the bottom. It is measured in metres, written m.

Frequency is the number of complete waves that pass a point every second, and it is measured in hertz, written Hz. If 5 waves go past you each second, the frequency is 5 Hz. The period is the time one complete wave takes to pass. In symbols, T = 1 ÷ f, with T in seconds. A wave of 5 Hz has a period of 1 ÷ 5 = 0.2 s.

Wave speed is how far the wave travels each second, measured in metres per second, written m/s. It is the speed at which the energy is transferred through the material. Pitch means how high or low a note sounds. A high frequency sound has a high pitch, like a whistle, and a low frequency sound has a low pitch, like a big drum.

Each second, f waves go past a point, and each wave is λ metres long, so the wave moves on by f × λ metres every second. In words: wave speed = frequency × wavelength. In symbols: v = f × λ, where v is in m/s, f is in Hz and λ is in m. The symbol λ is the Greek letter lambda. All waves obey this equation. A wave with a frequency of 4 Hz and a wavelength of 3 m has v = 4 × 3 = 12 m/s.

To find a missing frequency or wavelength, rearrange the equation. Frequency = wave speed ÷ wavelength, and wavelength = wave speed ÷ frequency. Always write the equation first, then put the numbers in, then give the unit. Each of those three steps can earn a mark.

Measuring the speed of waves

There are two ways to find the speed of a wave. You can measure the distance it travels and the time it takes, then use speed = distance ÷ time. Or you can measure the frequency and the wavelength, then use v = f × λ. Rearranging the equation is a useful skill here, so keep the formula triangle in mind.

To measure the speed of sound in air, two people stand a long measured distance apart in an open field, for example 200 m. One makes a loud bang, and the other starts a stopwatch when they see it and stops the watch when they hear it. Light arrives almost at once, so the time is the time for the sound. Speed = distance ÷ time. A long distance makes your reaction time matter less. Repeat the test and find the mean. The answer should be about 330 m/s.

An echo can also be used. An echo is a sound that bounces off a surface and comes back. The time covers the journey there and back, so distance to the wall = speed × time ÷ 2. If you know the distance, you can find the speed. If you know the speed, you can find the distance.

Many questions use 340 m/s for sound in air, so use the value you are given. With 340 m/s, an echo that returns after 0.6 s means the wall is 340 × 0.6 ÷ 2 = 102 m away. Ships use the same idea in water, where sound travels at about 1500 m/s.

To measure the speed of ripples, use a ripple tank. This is a shallow tank of water with a motor that makes ripples at a set frequency. A lamp above shines through the water onto white paper below, so the crests and troughs show as bright and dark lines. A strobe light or a phone video freezes the pattern.

Measure the distance across several wavelengths with a ruler and divide, which gives a more accurate wavelength. Then v = f × λ. For example, f = 15 Hz and λ = 0.012 m gives v = 15 × 0.012 = 0.18 m/s.

To measure waves in a solid, a vibration generator shakes one end of a stretched cord at a known frequency from a signal generator. Adjust until you see a steady pattern. Each loop of the pattern is half a wavelength, so measure several loops with a ruler and work out the wavelength. Then use v = f × λ again.

Check that your apparatus suits the job. A ruler is fine for the ripple pattern, but timing a ripple by hand is hard, so a strobe or video is better. A stopwatch is fine for sound over 200 m, but a reaction time of about 0.2 s would spoil a short distance. Choose apparatus with a small enough resolution and a long enough distance for the measurement.

The electromagnetic spectrum

Light is only one member of a big family of waves. They are called electromagnetic waves, or EM waves for short. EM waves are transverse waves that transfer energy from a source to an absorber. Sunlight carries energy from the Sun to your skin, and a microwave oven carries energy to your food.

EM waves can travel through a vacuum, which is empty space, and that is how sunlight reaches Earth across millions of kilometres. All types of EM wave travel at the same speed through a vacuum or air, about 300 000 000 m/s.

The whole family forms a continuous spectrum. The waves are grouped by their wavelength and frequency. In order, from the longest wavelength to the shortest, the groups are radio, microwave, infrared, visible light, ultraviolet, X-ray and gamma. As you go along the list, the frequency goes up and the wavelength goes down. Higher frequency waves carry more energy.

Visible light is the group that our eyes can detect. It runs from red, which has the longest wavelength, to violet, which has the shortest. Our eyes only detect this small part of the spectrum, so we cannot see the others even though they are all around us.

EM waves are made and absorbed by changes in atoms and nuclei. When an electron falls to a lower energy level in an atom, it gives out EM radiation. When an atom absorbs EM radiation, an electron moves to a higher level. Gamma rays come from changes in the nucleus of an atom.

Higher tier: radio waves are produced by oscillations in electrical circuits. An alternating current in a transmitter makes radio waves with the same frequency as the current. When a radio wave is absorbed by a receiving aerial, it creates an alternating current with the same frequency as the wave. That is how a radio picks up a signal.

Reflection, refraction and absorption

When a wave hits a surface, it can bounce back. This is called reflection. A mirror reflects light very well, which is why you can see yourself in it, and a hard wall reflects sound, which is why you hear echoes in an empty room with no carpet or curtains.

To describe reflection we draw a dotted line at right angles to the surface, called the normal. The angle of incidence is between the incoming ray and the normal, and the angle of reflection is between the bounced ray and the normal. A ray is just a thin line that shows which way the light is going.

The law of reflection says the angle of reflection equals the angle of incidence. If a ray hits a mirror at 30° to the normal, it leaves at 30° to the normal on the other side. Always measure from the normal, never from the mirror surface.

A wave that meets a different material can be absorbed, transmitted, reflected or refracted. A black surface absorbs most of the light that hits it, a mirror reflects it, and clear glass transmits it. Higher tier: how a material treats an EM wave depends on the wavelength. Glass lets visible light through but absorbs most ultraviolet. A metal surface reflects radio waves and microwaves, which is why a microwave oven has a metal case.

Refraction happens when a wave goes from one material into another and changes speed, which makes it change direction. Think of a shopping trolley rolling from the pavement onto grass at an angle. The wheel that reaches the grass slows first, so the whole trolley turns, and a light ray turns in just the same way when one side of it slows down.

Light slows down going from air into glass or water, so it bends towards the normal. Going back out into air it speeds up and bends away from the normal. The frequency stays the same, so the wavelength gets shorter in glass, and this refraction is why a straw in a glass of water looks bent.

To draw a ray diagram for refraction, draw the boundary and a dotted normal. Draw the incident ray up to the boundary. Then draw the refracted ray on the other side, closer to the normal if the wave slows down and further from the normal if it speeds up. A ray that travels along the normal goes straight on.

Higher tier: you can draw a wave as a set of parallel lines called wave fronts, where each line is a crest. If wave fronts meet a new material at an angle, one end slows down first. The wave fronts bunch closer together, because the wavelength gets shorter, and they turn. So the change of speed explains the change of direction. Wave fronts that hit the boundary head on slow down but do not turn.

Refraction in a rectangular glass block can be investigated like this. Place the block on a sheet of paper and draw round it. Shine a narrow ray from a ray box at the block at an angle. Mark the incident ray with two crosses and the emerging ray with two crosses. Remove the block and draw a normal at the point where the ray enters the glass. Join the crosses to show the path of the ray through the block. Measure the angle of incidence and the angle of refraction with a protractor, and repeat for different angles.

Light bends towards the normal as it enters the glass, because it slows down, and away from the normal as it leaves. The ray that comes out is parallel to the ray that went in, but shifted sideways, because the two sides of the block are parallel. Check that the normal and the angles are drawn carefully, and use a thin ray, a sharp pencil and crosses that are far apart.

Uses and dangers of EM waves

Radio waves carry television and radio signals. Microwaves send signals to satellites and cook food. Infrared is used in electrical heaters, for cooking food and in infrared cameras. Visible light carries data along optical fibres. Ultraviolet is used in energy efficient lamps and for sun tanning. X-rays and gamma rays are used for medical imaging and for treatments.

Higher tier: each wave suits its job for a reason. Radio waves are long, so they spread round hills and carry far. Microwaves pass through the atmosphere to satellites, and water in food absorbs them, so the food heats up. Infrared is absorbed by a surface, which warms. Light bounces along the inside of a thin glass fibre. X-rays pass through soft tissue but are absorbed by bone, so they make a shadow image of a broken bone. Gamma rays are very penetrating and ionising, so they can kill cancer cells.

You can investigate infrared with a Leslie cube. This is a metal cube filled with hot water, with a matt black side, a shiny black side, a matt white side and a shiny silver side. Hold an infrared detector the same distance from each side and read it. Use the same water, the same distance and the same detector, so the test is fair. The matt black side radiates the most infrared, and the shiny silver side radiates the least. Take care with the hot water.

Some EM waves are hazardous to body tissue. Ultraviolet can make skin age early and can increase the risk of skin cancer. X-rays and gamma rays are ionising radiation, which means they can damage cells. They can cause the mutation of genes and cancer. The effects depend on the type of radiation and on the size of the dose.

Radiation dose is a measure of the risk of harm from exposing the body to radiation. It is measured in sieverts, Sv. Doses are small, so they are usually given in millisieverts, mSv, where 1000 mSv = 1 Sv. A dental X-ray gives a tiny dose, about 0.005 mSv. A CT scan gives a much larger dose, of a few mSv. A bigger dose means a bigger risk. Doctors weigh the risk against the benefit, and radiographers stand behind a screen so that they are not exposed again and again.

The harmful effects are different for each type. Microwaves heat water in body cells, which can cause internal heating. Infrared can cause skin burns. Ultraviolet damages surface cells and the eyes, which can lead to skin cancer and eye damage such as cataracts. X-rays and gamma rays are ionising, so they can cause mutations and cancer. The danger rises with frequency.

More uses: gamma rays are used to sterilise medical equipment and food. X-rays are used to see broken bones. Ultraviolet is used in fluorescent lamps and to check security marks. Microwaves are used for cooking and for satellite signals, and radio waves for broadcasting and communications. Each use relies on the way the wave is absorbed or transmitted.

Recap

A wave transfers energy from place to place, and it does not carry matter. In a transverse wave the oscillation is at right angles to the direction of travel, and in a longitudinal wave it is parallel to it. Sound is longitudinal, while light and water ripples are transverse.

Amplitude is the height of a wave, wavelength is the length of one wave in metres, frequency is the number of waves per second in hertz, and period is T = 1 ÷ f. The wave speed equation is wave speed = frequency × wavelength, or v = f × λ. Measure the speed of sound with a long distance and a stopwatch, or with an echo, and measure ripples in a ripple tank.

For echoes, distance = speed × time ÷ 2, because the sound goes there and back. Reflection follows angle of reflection = angle of incidence, measured from the normal. Refraction is a change of direction caused by a change of speed, and light bends towards the normal as it slows down in glass.

All EM waves travel at the same speed in a vacuum. The order runs radio, microwave, infrared, visible, ultraviolet, X-ray, gamma. Ultraviolet, X-rays and gamma rays can harm body tissue, and X-rays and gamma rays can cause cancer. Higher tier: radio waves are made by and absorbed into alternating currents, and wave fronts explain refraction.

How this is asked in an exam: you are given a frequency and a wavelength and told to calculate the speed, or you are given an echo time and told to find a depth. Write the equation, substitute the numbers, then give the answer with its unit. Often one mark is for the halving, so always show your ÷ 2 step. For uses and dangers, give a use and a matching reason, such as X-rays pass through soft tissue but not bone.