5.1.1 Describing wave motion

What a wave is

1. A wave is a disturbance that moves through a material or through space, carrying energy from one place to another.
2. As a wave passes, each point it reaches makes an oscillation, moving back and forth about its rest position.
3. The points themselves stay in about the same place, so the wave transfers energy without carrying the material along with it.
4. Flicking one end of a long rope tied to a post sends a hump along the rope, yet each piece of rope only moves up and down as the hump goes by.
5. A wave that repeats regularly can be described fully using four quantities: amplitude, wavelength, frequency and period.
6. Amplitude and wavelength are distances, while frequency and period describe the timing of the oscillations.

Amplitude

1. As a wave passes, the displacement of each point keeps changing, from zero at the rest position to a maximum on one side and then a maximum on the other side.
2. On a drawing of a transverse wave, the peaks are called crests and the dips are called troughs.
3. The amplitude is the height of a crest above the rest position, which is the same as the depth of a trough below it.
4. Amplitude is always measured from the centre line, which marks the rest position, to the top of a crest or the bottom of a trough.
5. The vertical distance from the top of a crest to the bottom of a trough is twice the amplitude.
6. Amplitude is a distance, so it is measured in metres, $m$, or in centimetres, $cm$, for small waves.
7. A wave with a larger amplitude carries more energy, so a sound wave with a larger amplitude is louder and a water wave with a larger amplitude rocks a boat harder.
8. Changing the amplitude does not change how far apart the waves are or how often they arrive, so amplitude is independent of wavelength and frequency.

Wavelength

1. The wavelength is the length of one complete wave, measured along the direction in which the wave travels.
2. Wavelength has the symbol $\lambda$, the Greek letter lambda, and is measured in metres, $m$.
3. On a transverse wave, you can measure the wavelength from one crest to the next crest, or from one trough to the next trough.
4. Any pair of matching points works, as long as both points are at the same stage of the cycle, for example both on the centre line and both about to move upwards.
5. The distance from a crest to the next trough is only half a wavelength, because a crest and a trough are at opposite stages of the cycle.
6. Wavelengths vary enormously, from a few centimetres for ripples in a puddle to more than $100m$ for the long swells that roll onto the beaches of Cornwall.

Frequency and period

1. The frequency of a wave is how many complete waves pass a fixed point every second.
2. Frequency has the symbol $f$ and is measured in hertz, $Hz$.
3. A frequency of $50Hz$ means that 50 complete waves pass the point each second.
4. The frequency is set by the source of the wave, so a hand shaking a rope three times every second makes waves with a frequency of $3Hz$.
5. The period is the time taken for one complete wave to pass a point, which is also the time for one complete oscillation.
6. Period has the symbol $T$ and is measured in seconds, $s$.
7. Frequency and period describe the same repeating motion in two ways, so a high frequency always goes with a short period.
8. The two are linked by $T=\frac{1}{f}$, which can also be written as $f=\frac{1}{T}$.
9. A wave with a frequency of $4Hz$ has a period of $\frac{1}{4}=0.25s$, because four waves share each second equally.
10. The UK mains supply oscillates at $50Hz$, so each cycle of the mains lasts $\frac{1}{50}=0.02s$.

Reading wave graphs

1. Waves are usually drawn on one of two kinds of graph, so the first thing to check is the label on the horizontal axis.
2. A displacement-distance graph is like a photograph of the whole wave at one instant, with distance along the wave on the horizontal axis.
3. On a displacement-distance graph, the horizontal gap between neighbouring crests is the wavelength.
4. A displacement-time graph follows one single point as time passes, with time on the horizontal axis.
5. On a displacement-time graph, the horizontal gap between neighbouring crests is the period, which you can turn into a frequency using $f=\frac{1}{T}$.
6. On both kinds of graph, the amplitude is read from the vertical axis as the height of a crest above the zero line.
7. A wavelength can never be read from a displacement-time graph, and a period can never be read from a displacement-distance graph.

5.1.2 Wavelength and frequency

Defining wavelength

1. Wavelength is the distance from one point on a wave to the equivalent point on the next wave.
2. Two points are equivalent when they are at exactly the same stage of their oscillation, with the same displacement and moving in the same direction.
3. Crest to crest and trough to trough are the easiest equivalent pairs to spot, but any matching pair gives the same distance.
4. The symbol for wavelength is $\lambda$ and its SI unit is the metre, $m$.
5. Short wavelengths are often given in centimetres, where $1cm=0.01m$, or in millimetres, where $1mm=0.001m$.
6. Wavelength is a property of the wave in space, so it describes how stretched out the wave pattern is.

Measuring wavelength

1. Measuring a single wavelength with a ruler gives a large percentage uncertainty, because one wavelength is short compared with the smallest division on the ruler.
2. A more accurate method is to measure the distance across several complete waves and divide by the number of waves.
3. Count the gaps between crests rather than the crests themselves, because five crests in a row mark out only four wavelengths.
4. For example, if six crests span $30cm$, they mark out five wavelengths, so each wavelength is $30÷5=6.0cm$.
5. The distance must be measured along the direction in which the wave is travelling, not across it.

Defining frequency

1. Frequency is the number of complete waves passing a point each second.
2. This is the same as the number of complete oscillations each point makes per second, because every wave that passes makes the point go through one oscillation.
3. The symbol for frequency is $f$ and its unit is the hertz, $Hz$, where $1Hz$ means one complete wave per second.
4. Large frequencies are written with prefixes: $1kHz=1000Hz$, $1MHz=1000000Hz$ and $1GHz=1000000000Hz$.
5. Middle C on a piano has a frequency of about $262Hz$, so the piano string vibrates 262 times every second.
6. The frequency of a wave is fixed by the source that makes it, so it does not depend on the size of the waves.
7. Frequency is a property of the wave in time, so it describes how often the pattern repeats rather than how stretched out it is.
8. A louder sound from the same source has a larger amplitude but the same frequency, because the source is still vibrating at the same rate.

Measuring frequency

1. To find a frequency, pick a fixed point, such as a mark on the side of a ripple tank, and count the complete waves that pass it in a measured time.
2. Divide the number of complete waves by the time in seconds, so 24 waves in $8.0s$ gives a frequency of $3.0Hz$.
3. Counting over a longer time, such as $10s$ rather than $1s$, reduces the effect of your reaction time when starting and stopping the stopwatch.
4. If the period $T$ is known instead, the frequency is found from $f=\frac{1}{T}$.
5. Sound waves have frequencies far too high to count by eye, so they are measured electronically, for example with a microphone connected to a data logger.

5.1.3 Wave speed, frequency and wavelength

Wave speed

1. The wave speed is how fast the wave pattern, and the energy it carries, moves through the medium.
2. Wave speed has the symbol $v$ and is measured in metres per second, $m/s$.
3. Exam questions often call this quantity the wave velocity, and for GCSE calculations the two terms give the same number.
4. The speed of a wave is set by the medium it travels through, so waves of any frequency travel at the same speed in the same medium.
5. Ripples in a shallow tray of water travel at only a few tens of centimetres per second, while sound in air travels at about $340m/s$.

The wave equation

1. Wave speed, frequency and wavelength are linked by the wave equation, $v=f\lambda$.
2. In words, $wave\; speed=frequency\times wavelength$, with speed in $m/s$, frequency in $Hz$ and wavelength in $m$.
3. You must learn this equation by heart, because you are expected to recall it rather than look it up.
4. The equation works because each complete wave that leaves the source is exactly one wavelength long.
5. If the source makes $f$ waves every second, then $f$ wavelengths of new wave are added to the wave train every second.
6. The front of the wave therefore moves forward a distance of $f\times \lambda$ each second, which is its speed.
7. For example, a source making 5 waves per second, each $2m$ long, sends the front of the wave forward $10m$ every second.

How the quantities affect each other

1. The frequency is fixed by the source and the speed is fixed by the medium, so the wavelength is the quantity that adjusts to fit the equation.
2. In one medium, where the speed stays constant, frequency and wavelength are inversely proportional.
3. Doubling the frequency of the source halves the wavelength, because twice as many waves must fit into the same distance each second.
4. Lowering the frequency spreads the waves out, so the wavelength increases.
5. If the frequency stays the same but the wave moves into a medium where it travels faster, the wavelength increases in direct proportion to the speed.
6. Amplitude does not appear in the wave equation, so making a wave bigger does not change its speed, frequency or wavelength.

Waves in a ripple tank

1. A ripple tank lets you see water waves clearly enough to measure them.
2. A motor-driven dipper, or a straight wooden bar, touches the water surface and vibrates at a steady frequency, sending out a regular train of ripples.
3. A lamp above the tank shines through the water, and each crest acts like a lens, casting a bright line onto a white screen or sheet of paper below.
4. Each bright line marks a wavefront, so the spacing between neighbouring bright lines is one wavelength.
5. Straight wavefronts travel across the tank at right angles to a ray, which is an arrow drawn to show the direction the waves move.
6. The top-down view is what you see on the screen, so you measure the wavelength as the gap between neighbouring bright lines along the direction of the ray.

5.1.4 Wave speed problems

Using the wave equation

1. Every wave speed calculation uses the wave equation, $v=f\lambda$, which you must be able to recall.
2. Before you start, pick out the two quantities you have been given and the one you need to find.
3. To find the speed, multiply the frequency by the wavelength: $v=f\lambda$.
4. To find the frequency, divide the speed by the wavelength: $f=\frac{v}{\lambda }$.
5. To find the wavelength, divide the speed by the frequency: $\lambda =\frac{v}{f}$.
6. You can check a rearrangement with simple numbers, such as $v=10$, $f=2$ and $\lambda =5$, which fit all three forms.

Units and prefixes

1. The equation only gives the right answer when every quantity is in its standard unit: $m/s$ for speed, $Hz$ for frequency and $m$ for wavelength.
2. Convert centimetres to metres by dividing by $100$, so $45cm=0.45m$.
3. Convert millimetres to metres by dividing by $1000$, so $8mm=0.008m$.
4. Convert kilohertz to hertz by multiplying by $1000$, so $2.5kHz=2500Hz$.
5. Convert megahertz to hertz by multiplying by $1000000$, so $3.0MHz=3.0\times 10^{6}Hz$.
6. Very large or very small answers are clearest in standard form, so $0.0015m$ is written as $1.5\times 10^{-3}m$.
7. Give the final answer to a sensible number of significant figures, usually the same as the least precise value in the question.

Multi-step problems

1. Harder questions do not give you $f$ and $\lambda$ directly, so you must work them out from other information first.
2. If the period is given, find the frequency first using $f=\frac{1}{T}$.
3. If a distance covering several waves is given, divide it by the number of waves to get one wavelength.
4. If you are asked how long a wave takes to travel a distance, find its speed and then use $time=\frac{distance}{speed}$.
5. Writing down each intermediate value with its unit stops you losing track, and lets the examiner award marks for each correct step.

5.1.5 Transverse and longitudinal waves

Transverse waves

1. In a transverse wave, the oscillations are at right angles, or perpendicular, to the direction in which the wave travels and transfers energy.
2. If a transverse wave moves from left to right along a rope, each piece of rope moves up and down.
3. The points displaced furthest one way form the crests, and the points displaced furthest the other way form the troughs.
4. A transverse wave is drawn as a smooth up-and-down curve, with the wavelength measured from one crest to the next.
5. Examples of transverse waves include waves on a stretched string or rope, ripples on the surface of water and electromagnetic waves such as light.
6. A guitar string shows the idea clearly, because the string vibrates sideways while the wave travels along its length.

Longitudinal waves

1. In a longitudinal wave, the oscillations are parallel to the direction in which the wave travels and transfers energy.
2. The particles move backwards and forwards along the same line that the wave is moving along.
3. As the particles move, they bunch up in some places and spread out in others, forming a repeating pattern of compressions and rarefactions.
4. In a compression the particles are close together, so the pressure and density there are higher than normal.
5. In a rarefaction the particles are further apart, so the pressure and density there are lower than normal.
6. The compressions and rarefactions travel along, but each particle only moves a short distance back and forth about its rest position.
7. Sound waves are longitudinal, whether they travel through air, water or a solid.
8. The wavelength of a longitudinal wave is the distance from the centre of one compression to the centre of the next compression.
9. The amplitude of a longitudinal wave is the greatest distance a particle moves from its rest position along the direction of travel.
10. A graph of pressure against distance for a sound wave looks like a transverse wave, with peaks at the compressions, but this is only a way of plotting the data and not a picture of how the particles move.

Comparing the two types

1. The two types of wave are told apart by comparing the direction of oscillation with the direction of energy transfer.
2. In a transverse wave these two directions are perpendicular, while in a longitudinal wave they are parallel.
3. Transverse waves are described using crests and troughs, while longitudinal waves are described using compressions and rarefactions.
4. Both types transfer energy from place to place without carrying the material of the medium along with them.
5. Both types are described using the same quantities, amplitude, wavelength, frequency and period, and both obey $v=f\lambda$.

5.1.6 Sound waves crossing between media

Sound needs a medium

1. A sound wave is a longitudinal wave made when a vibrating object pushes and pulls on the particles around it.
2. Each particle passes the vibration on to its neighbours, so sound can only travel where there are particles to carry it.
3. The material a wave travels through is its medium, and sound can travel through solids, liquids and gases.
4. Sound cannot travel through a vacuum, because there are no particles to pass the vibrations on.
5. An electric bell ringing inside a sealed glass jar goes quiet as the air is pumped out, even though you can still see the hammer striking the bell.

Speed of sound in different media

1. The speed of sound depends on the medium, and it is usually fastest in solids, slower in liquids and slowest in gases.
2. Typical values are about $340m/s$ in air, about $1500m/s$ in water and about $6000m/s$ in steel.
3. In a solid, the particles are packed closely together and held by strong forces, so each vibration is passed to the next particle very quickly.
4. In a gas, the particles are far apart and only pass on a vibration when they collide, so the disturbance travels much more slowly.
5. The speed of sound in a gas also increases with temperature, because faster-moving particles pass the vibration on sooner.

Crossing a boundary

1. When sound passes from one medium into another, its speed changes, because the new medium passes vibrations along at a different rate.
2. The frequency does not change, because the particles at the boundary are forced to vibrate at the same rate as the particles hitting them.
3. Every vibration that reaches the boundary in one second is passed on in that same second, so the number of waves per second is the same on both sides.
4. Since $v=f\lambda$ and $f$ stays fixed, the wavelength must change in the same proportion as the speed.
5. If the sound speeds up as it enters the new medium, its wavelength increases, so the compressions spread further apart.
6. If the sound slows down as it enters the new medium, its wavelength decreases, so the compressions crowd closer together.
7. For the same frequency, $\frac{{\lambda }_2}{{\lambda }_1}=\frac{v_2}{v_1}$, so tripling the speed triples the wavelength.
8. A swimmer under water hears a whistle from the poolside as the same note, because the frequency is unchanged, even though its wavelength in the water is more than four times longer.

5.1.7 Reflection, transmission and absorption at interfaces

Waves at an interface

1. An interface is the boundary between two materials, such as air and glass, water and the seabed, or air and a brick wall.
2. When a wave reaches an interface, its energy can be reflected, transmitted or absorbed.
3. In reflection, the wave bounces back into the material it came from.
4. In transmission, the wave passes through the interface and carries on into the second material.
5. In absorption, energy from the wave is transferred to the material, usually increasing its thermal energy store so it warms up slightly.
6. At most interfaces all three happen at once, with the wave's energy shared between them.
7. A window transmits most of the light that reaches it, reflects a little so you can see a faint reflection, and absorbs a small amount.
8. How the energy is shared depends on the two materials, on the wavelength of the wave and on the angle at which it arrives.
9. Energy is always conserved, so the energy reflected, transmitted and absorbed adds up to the energy that arrived.

Reflection and echoes

1. Reflection is strongest when a wave meets a surface it cannot easily pass into, such as light hitting a mirror or sound hitting a hard wall.
2. To describe a reflection, you draw a normal, an imaginary line at right angles to the surface where the wave strikes it.
3. The angle of incidence is measured between the incoming ray and the normal.
4. The angle of reflection is measured between the reflected ray and the normal.
5. For a smooth, flat surface, the law of reflection states that the angle of incidence is equal to the angle of reflection.
6. A reflected sound wave is called an echo, and you hear it as a separate sound if it returns more than about $0.1s$ after the original.
7. Hard, smooth surfaces such as tiled walls reflect sound well, which is why a school sports hall or a swimming pool sounds so echoey.
8. Soft, uneven materials such as curtains, carpets and foam panels absorb much more of the sound, so recording studios and cinemas line their walls with them.

Ultrasound and sonar

1. Ultrasound is sound with a frequency above $20000Hz$, which is too high for humans to hear.
2. When ultrasound reaches the boundary between two different materials, part of it is reflected and the rest is transmitted onwards.
3. Each boundary the ultrasound reaches sends back a weaker echo, so a single pulse produces a series of echoes from boundaries at different depths.
4. Timing each echo shows how far away each boundary is, which allows structures that cannot be seen directly, such as an unborn baby, to be mapped.
5. Sonar uses the same idea under water, with a ship sending a pulse of sound or ultrasound down to the seabed and timing how long the echo takes to return.
6. The pulse travels down to the seabed and back up again, so the depth is half of the total distance the pulse travels.
7. This gives $depth=\frac{speed\times time}{2}$.
8. Fishing boats use sonar to find shoals of fish, and survey ships use it to map the shape of the seabed and to find shipwrecks.

Refraction at an interface

1. When a transmitted wave crosses an interface at an angle, it can change direction, and this is called refraction.
2. Refraction happens because the wave changes speed as it moves into the new material.
3. Light slows down as it passes from air into glass and bends towards the normal, then speeds up as it leaves and bends away from the normal.
4. A wave that meets the interface along the normal changes speed but does not change direction.

5.1.8 Sound waves and vibrations in solids

Vibrations and sound

1. A sound wave and the vibration of a solid object are two forms of the same disturbance, and each can be turned into the other.
2. A vibrating surface in contact with air pushes on the air as it moves outwards and pulls back as it moves inwards.
3. Moving outwards squeezes the nearby air particles together into a compression.
4. Moving back inwards leaves extra space, so the air particles spread out into a rarefaction.
5. Each cycle of the surface's vibration produces one compression and one rarefaction, so the sound wave has the same frequency as the vibrating object.
6. The reverse also happens, because the changing pressure of a sound wave pushes and pulls on any solid surface it reaches and makes that surface vibrate.
7. In both directions energy is transferred, but no material travels from the source to the receiver.

Solids producing sound

1. A loudspeaker contains a light paper or plastic cone that an electrical signal forces to vibrate back and forth, sending sound waves into the air.
2. A plucked guitar string vibrates, but the thin string moves very little air on its own.
3. The string passes its vibrations through the bridge to the hollow wooden sound box, whose large surface pushes on far more air and makes the sound much louder.
4. A tuning fork has two metal prongs that vibrate at one fixed frequency when struck, producing a pure note.
5. Pressing the base of a vibrating tuning fork onto a wooden table makes the note louder, because the large table top is forced to vibrate and pushes on more air.
6. A drum skin vibrates when it is struck, and its large area creates strong compressions and rarefactions in the air.

Sound making solids vibrate

1. When sound waves reach a microphone, they make a thin, flexible diaphragm vibrate, and the microphone turns these vibrations into an electrical signal.
2. A loud bass note from a passing car can make a shop window rattle, because the sound waves force the glass to vibrate.
3. Music from next door reaches you because the sound waves make the dividing wall vibrate, the vibrations travel through the bricks, and the far side of the wall then produces new sound waves in your room.
4. Your own ear works in the same way, using a chain of solid parts to turn sound waves into vibrations and then into electrical signals.

Structure of the ear

1. The outer ear, or pinna, is the visible flap that collects sound waves and funnels them into the ear canal.
2. Sound waves travel down the air-filled ear canal to the eardrum, a thin membrane stretched across its inner end.
3. The changing pressure of the sound wave makes the eardrum vibrate at the same frequency as the sound.
4. In the air-filled middle ear, the eardrum is linked to three tiny bones called the ossicles: the hammer, the anvil and the stirrup.
5. The ossicles act as levers that pass the vibrations along and amplify them, increasing the force of each vibration.
6. The stirrup presses against a small membrane called the oval window, which is the entrance to the inner ear.
7. The vibrating oval window sets up waves in the fluid inside the cochlea, a coiled tube in the inner ear.
8. Tiny hair cells lining the cochlea are moved by the fluid and produce electrical signals.
9. The auditory nerve carries these signals to the brain, which interprets them as sound.
10. Along this route the disturbance changes form several times: a sound wave in air, vibrations of solid parts, waves in the fluid of the cochlea, and finally electrical signals.

5.1.9 Frequency range and human hearing

Why the frequency range is limited

1. Every solid part that converts sound into vibration, such as an eardrum or a microphone diaphragm, has mass and stiffness.
2. Together, the mass and stiffness give the part a natural frequency at which it vibrates most easily.
3. When sound drives the part at or near its natural frequency, it vibrates with a large amplitude, an effect called resonance.
4. The further the frequency of the sound is from the natural frequency, the smaller the amplitude of the vibration becomes.
5. At very high frequencies, the part's mass gives it too much inertia to reverse direction quickly enough, so it barely moves.
6. At very low frequencies, the slow pressure changes are too weak compared with the part's stiffness to make it vibrate usefully.
7. Outside a certain range of frequencies, the vibrations are so small that no useful signal is produced.
8. This is why every microphone and loudspeaker has a stated frequency range, and why small earphones struggle to reproduce deep bass notes.
9. The same limit applies in reverse, because a solid can only produce sound waves over the range of frequencies at which it can vibrate.

The range of human hearing

1. The human ear can only turn sound into nerve signals over a limited range of frequencies, called the audible range.
2. For a young person with healthy hearing, this range is about $20Hz$ to $20000Hz$, or $20kHz$.
3. Sound below $20Hz$ is called infrasound, and sound above $20000Hz$ is called ultrasound.
4. Infrasound and ultrasound are still sound waves that carry energy, but the parts of the ear cannot respond to them strongly enough to produce signals.
5. Within the audible range, the frequency of a sound sets its pitch, so a higher frequency is heard as a higher note.
6. The ear is most sensitive to frequencies of a few thousand hertz, which helps you pick out the sounds of speech.
7. Other animals have ears built differently, so dogs can hear up to about $45000Hz$, bats hear well above $100000Hz$, and elephants communicate using infrasound.

How hearing changes with age

1. Inside the cochlea, rows of hair cells each respond best to a particular frequency.
2. Hair cells near the entrance of the cochlea respond to high frequencies, while those deep inside the coil respond to low frequencies.
3. Hair cells are gradually damaged over a lifetime and, unlike many cells in the body, they are not replaced.
4. The cells that detect high frequencies are usually lost first, so the upper limit of hearing falls as people get older.
5. By middle age many adults cannot hear sounds above about $15000Hz$, and the limit keeps dropping with age.
6. The eardrum and ossicles can also become stiffer with age, so they pass on vibrations less well.
7. Repeated exposure to loud sound, such as from concerts, power tools or earphones turned up high, damages hair cells faster and brings hearing loss on earlier.
8. Some UK shops have used devices that give out a tone of about $17000Hz$ to stop groups gathering outside, because most teenagers can hear it while most older adults cannot.

5.1.10 Modelling waves with water ripples and sound

Ripples as a model of transverse waves

1. Waves on the surface of water are slow and easy to see, so ripples are used as a model of transverse waves in general.
2. As a ripple passes, each bit of the water surface moves mainly up and down while the ripple itself travels across the surface.
3. The oscillation of the surface is at right angles to the direction of travel, which is the key feature of a transverse wave.
4. Real water waves are not perfectly transverse, because the water also moves slightly back and forth, so each bit of the surface traces out a small loop.
5. A ripple tank makes ripples visible, because a lamp above the tank shines through the water and each crest focuses the light into a bright line on a screen below.
6. The bright lines are the wavefronts, so the spacing between them shows the wavelength directly.
7. A stroboscope flashing at the same frequency as the dipper makes the pattern appear to freeze, which makes the wavelength much easier to measure.
8. Ripples in shallow water travel at only a few tens of centimetres per second, so their speed can be measured with simple equipment.

Sound in air is longitudinal

1. Sound cannot be seen, but it travels through air as a longitudinal wave.
2. A vibrating source pushes and pulls on the air, producing compressions and rarefactions that move away from it.
3. Each air particle vibrates backwards and forwards parallel to the direction the sound travels.
4. Sound in air travels at about $340m/s$, roughly a thousand times faster than ripples in a tank, so measuring its speed needs a long distance or very fast electronic timing.
5. You notice the speed of sound when you see a firework burst before you hear the bang, because light reaches you almost instantly while sound takes about $3s$ to travel $1km$.

Measuring the speed of each wave

1. Both speeds are found from $speed=\frac{distance}{time}$, or from $v=f\lambda$ when the frequency and wavelength can be measured.
2. For ripples, the distances and times are short, so filming the tank gives far more reliable timing than a hand-held stopwatch.
3. For sound, a stopwatch is far too slow over a short distance, so you need either a very long distance or an electronic timer triggered by microphones.

Refraction in a ripple tank

1. The speed of ripples depends on the depth of the water, and they travel more slowly in shallower water.
2. Placing a sheet of clear plastic or glass in part of the tank creates a shallow region with a sharp boundary.
3. Ripples crossing into the shallow region slow down, and because their frequency is fixed by the dipper, their wavelength becomes shorter.
4. If the wavefronts meet the boundary at an angle, the part of each wavefront that reaches the shallow water first slows down first, so the wavefront swings round and changes direction.
5. This change of direction caused by a change of speed is refraction, the same effect that bends light at the surface of a glass block.

5.1.11 Evidence that the wave travels, not the medium

The wave travels, not the medium

1. A wave transfers energy from one place to another, but the medium it travels through does not travel with it.
2. Each particle of the medium oscillates about its rest position and passes the disturbance on to the next particle.
3. Once the wave has passed, every particle is back where it started, so there is no overall movement of the material.
4. A Mexican wave at a football ground works in the same way, because the wave races round the stadium while each fan only stands up and sits down in their own seat.
5. Water particles and air particles are far too small to watch, so the evidence comes from objects that move along with them.

Evidence from water ripples

1. A cork, a leaf or a small piece of paper floating on water moves exactly as the surface beneath it moves.
2. As ripples pass, the floating object bobs up and down, with a slight back-and-forth movement.
3. The floating object is not carried along with the ripples, and once they have passed it is still in about the same place.
4. If the water itself travelled with the ripples, the floating object would be swept across to the far side.
5. A duck sitting on a pond rises and falls as ripples from a thrown stone pass beneath it, but it does not drift towards the bank.
6. This shows that the ripple, and the energy it carries, travels across the water while the water stays where it is.

Evidence from sound in air

1. Air particles are invisible, so the evidence comes from the effect sound has on something light that sits in the air.
2. A candle flame placed in front of a loudspeaker playing a loud, low note flickers backwards and forwards, but it is not blown away from the speaker.
3. The flame moves back and forth because the air around it vibrates back and forth as compressions and rarefactions pass through it.
4. If the air were flowing away from the loudspeaker, the flame would lean steadily away from it, as it does in a draught.
5. Wind is a flow of air from one place to another, while a sound wave is a vibration of air in place, which is why loud music does not blow your hair back.
6. A ribbon tied to a stretched slinky shows the same thing for any longitudinal wave, because it moves back and forth as compressions pass but stays at the same point on the spring.