Ripples as a model of transverse waves
Definition
Ripple tank
A shallow tank of water with a transparent base in which a vibrating dipper makes ripples that can be observed and measured.
Definition
Wavefront
A line joining points on a wave that are at the same stage of their oscillation, such as a line along one crest.
Definition
Stroboscope
A lamp that flashes at an adjustable frequency so that a repeating motion, such as a train of ripples, appears to stand still.
- Waves on the surface of water are slow and easy to see, so ripples are used as a model of transverse waves in general.
- As a ripple passes, each bit of the water surface moves mainly up and down while the ripple itself travels across the surface.
- The oscillation of the surface is at right angles to the direction of travel, which is the key feature of a transverse wave.
- 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.
- 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.
- The bright lines are the wavefronts, so the spacing between them shows the wavelength directly.
- A stroboscope flashing at the same frequency as the dipper makes the pattern appear to freeze, which makes the wavelength much easier to measure.
- 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
Definition
Longitudinal wave
A wave in which the oscillations are parallel to the direction in which the wave transfers energy.
Definition
Compression
A region of a longitudinal wave where the particles are pushed closer together than normal.
Definition
Rarefaction
A region of a longitudinal wave where the particles are spread further apart than normal.
- Sound cannot be seen, but it travels through air as a longitudinal wave.
- A vibrating source pushes and pulls on the air, producing compressions and rarefactions that move away from it.
- Each air particle vibrates backwards and forwards parallel to the direction the sound travels.
- Sound in air travels at about 340 m/s340\ \text{m/s}340 m/s, roughly a thousand times faster than ripples in a tank, so measuring its speed needs a long distance or very fast electronic timing.
- 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 3 s3\ \text{s}3 s to travel 1 km1\ \text{km}1 km.
Measuring the speed of each wave
- Both speeds are found from speed=distancetime\text{speed} = \dfrac{\text{distance}}{\text{time}}speed=timedistance, or from v=fλv = f\lambdav=fλ when the frequency and wavelength can be measured.
- For ripples, the distances and times are short, so filming the tank gives far more reliable timing than a hand-held stopwatch.
- 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.
Practical
Speed of water ripples
- Aim: to measure the speed of water ripples by timing a single wavefront over a measured distance.
- Apparatus: a ripple tank, water, a straight dipper with a motor and low-voltage supply, a lamp, a white screen or sheet of paper, a metre ruler, and a mobile phone that can record slow-motion video.
- Method:
- Fill the tank to a constant depth of about 5 mm5\ \text{mm}5 mm and check with a spirit level that it is level.
- Lay the metre ruler across the bottom of the tank in the direction the ripples will travel, so that its shadow appears on the screen at the same scale as the ripples.
- Choose two marks on the ruler's shadow that are 40 cm40\ \text{cm}40 cm apart.
- Switch on the dipper briefly to send a short train of ripples across the tank.
- Film the screen in slow motion, then play the video back and find the time for one bright wavefront to travel from the first mark to the second.
- Calculate the speed using v=dtv = \dfrac{d}{t}v=td.
- Repeat at least three times and calculate a mean, leaving out any anomalous result.
- Second method: freeze the pattern with a stroboscope or a photograph, measure across ten wavelengths, read the frequency from the dipper's signal generator and calculate v=fλv = f\lambdav=fλ.
- Results: ripples in shallow water typically travel at about 0.2 m/s0.2\ \text{m/s}0.2 m/s to 0.3 m/s0.3\ \text{m/s}0.3 m/s, and the two methods should give similar values.
- Watch out: the pattern on the screen is magnified by the spreading light, so always measure against the shadow of the ruler rather than a ruler lying on the screen.
- Safety: keep the electrical equipment away from the water and wipe up any spills straight away.
Practical
Speed of sound in air
- Aim: to measure the speed of sound in air using two microphones and an electronic timer.
- Apparatus: two microphones, a fast electronic timer or data logger that reads to at least 0.0001 s0.0001\ \text{s}0.0001 s, a tape measure, and two wooden blocks to make a sharp sound.
- Method, two microphones:
- Place the two microphones in a straight line with the sound source, with a measured gap of 1.00 m1.00\ \text{m}1.00 m between them.
- Connect the first microphone so that it starts the timer and the second so that it stops it.
- Clap the blocks together sharply just beyond the first microphone, on the same line.
- Record the time interval, which is the time the sound takes to travel from the first microphone to the second.
- Repeat several times, calculate a mean time and use v=dtv = \dfrac{d}{t}v=td to find the speed.
- Repeat with larger gaps between the microphones to check that the speed stays the same.
- Method, echo:
- Stand at a measured distance, such as 50 m50\ \text{m}50 m, from a large, flat wall in an open space.
- Clap at a steady rhythm, adjusting it until each clap happens exactly as the echo of the previous clap returns.
- Have a partner time 20 claps, then divide by 20 to find the time between claps.
- In that time the sound travels to the wall and back, so the distance is 2×50=100 m2 \times 50 = 100\ \text{m}2×50=100 m.
- Results: the speed of sound in air is about 340 m/s340\ \text{m/s}340 m/s, so with a 1.00 m1.00\ \text{m}1.00 m gap the timer reads about 0.0029 s0.0029\ \text{s}0.0029 s.
- Watch out: a soft or drawn-out sound may not trigger the microphones cleanly, so use a single sharp sound and keep the room quiet.
- Safety: keep the sounds at a sensible volume to protect your hearing, and do the echo method well away from roads.
Refraction in a ripple tank
Definition
Refraction
The change in direction of a wave as it crosses an interface at an angle, caused by a change in its speed.
- The speed of ripples depends on the depth of the water, and they travel more slowly in shallower water.
- Placing a sheet of clear plastic or glass in part of the tank creates a shallow region with a sharp boundary.
- Ripples crossing into the shallow region slow down, and because their frequency is fixed by the dipper, their wavelength becomes shorter.
- 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.
- 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.
Practical
Investigating refraction of ripples
- Aim: to observe how ripples change speed, wavelength and direction when they pass from deep water into shallow water.
- Apparatus: a ripple tank, water, a straight dipper and motor, a lamp, a white screen, a rectangular sheet of clear plastic about 5 mm5\ \text{mm}5 mm thick, a stroboscope or camera, a metre ruler and a protractor.
- Method:
- Lay the plastic sheet in one half of the tank and add water until it covers the sheet by about 1 mm1\ \text{mm}1 mm, giving a deep region and a shallow region.
- Set the dipper running so that straight wavefronts travel towards the edge of the sheet, first with the wavefronts parallel to the edge.
- Freeze the pattern with the stroboscope or a photograph and measure the wavelength in each region across several wavefronts.
- Turn the sheet so that its edge is at about 45∘45^\circ45∘ to the oncoming wavefronts.
- Freeze the pattern again, draw the direction of travel on each side of the boundary, and use the protractor to measure how much the direction changes.
- Results: the wavelength is shorter over the sheet, showing that the ripples slow down in shallow water, and when they arrive at an angle the wavefronts change direction at the boundary.
- Variables: the depth of water over the sheet and the frequency of the dipper are kept the same, so that any change is caused by the boundary alone.
- Watch out: if the water over the sheet is too deep the change in speed is too small to see, and if it is too shallow the ripples die away.
- Safety: use a low-voltage supply for the motor and lamp, and keep mains plugs well away from the tank.
Example
Speed of sound from an echo
- A student stands 85 m85\ \text{m}85 m from a tall brick wall and claps once.
- The echo is heard 0.50 s0.50\ \text{s}0.50 s after the clap.
- The sound travels to the wall and back, so the total distance is twice the distance to the wall.
Common Mistake
- Do not describe a ripple as a wave that travels up and down, because the ripple travels across the water while the surface moves up and down.
- Do not forget to double the distance in an echo method, because the sound travels to the wall and back again.
Exam technique
Describing a speed measurement
- State the two quantities you measure, a distance and a time, and name the equipment for each.
- Say how you make the timing accurate, such as slow-motion video for ripples or microphones and an electronic timer for sound.
- Mention repeating the measurement and calculating a mean.
- Finish with the equation you use to calculate the speed.
Self review
- Why are ripples on water used as a model of transverse waves?
- How do air particles move as a sound wave passes through them?
- Why can a hand-held stopwatch not be used to time sound over a distance of 1 m1\ \text{m}1 m?
- What happens to the wavelength of ripples as they pass into shallower water?
- Why is the distance doubled when an echo is used to measure the speed of sound?
