Answers · Waves in a ripple tank

Waves and how they move — answer key

Check meaning, not exact wording. These are teaching points, not official Cambridge marks.

1. VQ1 · Practice

Model answer. The ripples carry energy across the pond, but not the water. As each ripple passes, the water under the leaf rises and falls and ends up where it started, so the leaf bobs up and down about the same place while the ripples travel on past it.

A full answer includes

I chose: it bobs up and down about the same place.
I did not choose that the ripples carry it to the edge.

Also accept

it bobs up and down about the same place

Watch for

“It is carried along with the ripples to the edge of the pond.” — A wave carries energy, not the water. The water, and the leaf with it, rises and falls and ends up where it started.
“It stays completely still while the ripples pass under it.” — The energy passing through makes the water rise and fall where it is, so the leaf moves too.
“It is pushed back towards the place where the stone landed.” — Nothing pushes the water back. Each bit of water only rises and falls about its own place as the ripples pass.

2. VQ2 · Practice

Model answer. The cup at the far end tips over, so something reached the far end: the pulse carried energy along the hose. The ladybird moved sideways and back but ended where it started, so the hose under it only vibrated about its own place and was not carried along. Waves transfer energy without transferring matter. Row A.

A full answer includes

I chose row A.
I did not choose row D, where the ladybird moving sideways is the evidence that the hose stayed in place.

Also accept

Row A

Watch for

“Row B.” — The columns are swapped. Tipping the cup needs something to reach the far end: the energy. The ladybird back in its place shows that the hose under it was not carried along.
“Row C.” — The ladybird moving sideways happens halfway along, not at the far end, and the cup tipping over shows that something arrived, not that the hose stayed in place.
“Row D.” — The cup tipping over does show that energy arrived. But moving sideways on its own does not show the hose stayed in place: ending where it started does.

3. VQ3 · Practice

Model answer. (a) The frequency is the number of vibrations each second: f = 12 ÷ 8.0 s = 1.5 Hz. (b) The distance from one crest to the next is the wavelength, λ = 0.50 m. So v = fλ = 1.5 Hz × 0.50 m = 0.75 m/s.

Checked automatically

(a) Frequency: 1.5 Hz (within ±0.02 Hz)
- Common wrong answer 0.67 : That is 8.0 s ÷ 12, the time for one vibration. The frequency is the number of vibrations each second.
- Common wrong answer 96 : You multiplied the count by the time. The frequency is the count divided by the time.
- Common wrong answer 12 : That is the number of vibrations in 8.0 s, not in one second.
(b) Wave speed: 0.75 m/s (within ±0.01 m/s)
- Common wrong answer 0.33 : That is λ ÷ f, or 0.67 × 0.50. Use v = fλ, with f in vibrations per second.
- Common wrong answer 3.0 : That is f ÷ λ. The speed is v = fλ: multiply the frequency by the wavelength.
- Common wrong answer 6.0 : You used 12 as the frequency. Use the number of vibrations each second.

A full answer includes

(a) I divided the 12 vibrations by the 8.0 s.
(a) I wrote 1.5 Hz.
(a) I did not divide 8.0 s by 12.
(b) I took the crest-to-crest distance, 0.50 m, as the wavelength.
(b) I wrote v = fλ = 1.5 Hz × 0.50 m.
(b) I wrote 0.75 m/s.

Also accept

(a) 1.5 Hz (b) 0.75 m/s

Watch for

“The frequency is 8.0 s ÷ 12 = 0.67 Hz.” — That is the time for one vibration. The frequency is the number of vibrations each second.
“The wave speed is the wavelength divided by the frequency.” — The wave speed is v = fλ: the frequency times the wavelength.

4. VQ4 · Practice

Options as numbered on the pupil sheet: 1 — Longitudinal; 2 — Transverse.

Model answer. Electromagnetic radiation, such as light, water waves and seismic S-waves are modelled as transverse: the vibration is at right angles to the direction of travel. Sound and seismic P-waves are longitudinal: the vibration is parallel to the direction of travel. Pushing and pulling the end of a slinky makes the coils move to and fro along the slinky, so that wave is longitudinal too.

A full answer includes

I matched light from the Sun to transverse.
I matched sound from a drum to longitudinal.
I matched the seismic P-wave to longitudinal.
I matched the seismic S-wave to transverse.
I matched waves on the surface of the sea to transverse.
I matched the push-and-pull wave on the slinky to longitudinal.
I did not swap the P-wave and the S-wave.

Also accept

light transverse; sound longitudinal; P-wave longitudinal; S-wave transverse; sea waves transverse; push-and-pull slinky longitudinal

Watch for

“Seismic P-waves are transverse and S-waves are longitudinal.” — It is the other way round: P-waves (primary, they arrive first) are longitudinal, like sound; S-waves (secondary) are transverse.
“Sound is transverse, like a wave on a rope.” — In sound the air particles vibrate to and fro along the direction the sound travels, so sound is longitudinal.
“The wave made by pushing and pulling the end of a slinky is transverse.” — Pushing and pulling moves each coil to and fro along the slinky, parallel to the direction the wave travels: that wave is longitudinal.
“Waves on the surface of the sea are longitudinal.” — The sea surface rises and falls while the waves travel across it, at right angles to that travel: water waves are modelled as transverse.
“Light from the Sun is longitudinal.” — Light, like all electromagnetic radiation, is modelled as transverse.

5. VQ5 · Practice

Model answer. Sound is a longitudinal wave. As it passes, each air particle vibrates to and fro about its own place, along the direction in which the sound travels: the line from the whistle to the player. The particles are not carried to the player; they pass the energy on.

A full answer includes

I chose: they vibrate to and fro along the line from the whistle to the player.
I did not choose that they vibrate at right angles to that line.

Also accept

they vibrate to and fro along the line from the whistle to the player

Watch for

“They vibrate up and down, at right angles to the line between them.” — That would be a transverse wave. Sound is longitudinal: the particles vibrate parallel to the direction the sound travels.
“They are carried along the line from the whistle to the player.” — The air is not carried to the player. Each particle vibrates about its own place and passes the energy on.
“They stay still, because only the energy of the sound moves on.” — The energy is passed on because the particles vibrate. They move to and fro about their own places.

6. VQ28 · Practice

Model answer. The earthquake is due north, so both waves travel from north to south to reach the seismometer. X shakes the ground north and south, parallel to its direction of travel: X is longitudinal, and the longitudinal seismic wave is the P-wave. Y shakes the ground east and west, at right angles to its direction of travel: Y is transverse, an S-wave. Row B.

A full answer includes

I chose row B.
I did not choose row A, which takes the north–south shaking as being at right angles to the travel.

Also accept

Row B

Watch for

“Row A.” — The waves travel from north to south, so X, which shakes the ground north and south, vibrates parallel to its travel. X is longitudinal: a P-wave.
“Row C.” — The names are right but the kinds are swapped. X vibrates along its direction of travel, so it is longitudinal; P-waves are longitudinal and S-waves transverse.
“Row D.” — X is longitudinal, but the longitudinal seismic wave is the P-wave, not the S-wave.

7. VQ6 · Practice

Model answer. (a) Longitudinal. The wave travels up the spring, and each coil vibrates up and down, which is along the spring: the vibration is parallel to the direction of propagation. (b) Move the lower end of the spring from side to side, again and again, at right angles to the length of the spring. (c) The coil moves from side to side about its own place, at right angles to the direction in which the wave travels up the spring, and ends up where it started.

A full answer includes

(a) I wrote longitudinal.
(a) I gave the reason: the coils vibrate parallel to the direction the wave travels, up the spring.
(a) I did not call it transverse just because the coils move up and down.
(b) I wrote: move the lower end from side to side, at right angles to the spring.
(c) I wrote that the coil moves from side to side.
(c) I wrote that it moves about its own place and is not carried up the spring.

Also accept

(a) longitudinal: vibration parallel to the travel (b) move the lower end from side to side (c) side to side about its own place

Watch for

“The wave in (a) is transverse, because the coils move up and down.” — Up and down is along this spring, the same direction as the wave travels. Compare the vibration with the direction of travel, not with the floor.
“In (b) the coil is carried up the spring with the wave.” — Each coil vibrates about its own place; only the energy travels up the spring.

8. VQ7 · Practice

Options as numbered on the pupil sheet: 1 — The wavelength; 2 — A crest; 3 — A trough; 4 — Twice the amplitude; 5 — The amplitude.

Model answer. A is a highest point, a crest (or peak), and B is a lowest point, a trough. C runs from one crest to the next, which is one wavelength. D runs from the rest line up to a crest: that is the amplitude. E runs from a trough up to a crest, which is twice the amplitude.

A full answer includes

I matched A to a crest.
I matched B to a trough.
I matched C to the wavelength.
I matched D to the amplitude.
I matched E to twice the amplitude.
I did not match E to the amplitude.

Also accept

A crest; B trough; C wavelength; D amplitude; E twice the amplitude

Watch for

“E is the amplitude, because it is the whole height of the wave.” — From a trough to a crest is twice the amplitude. The amplitude is from the rest line to a crest.
“The wavelength is the distance from a crest to the next trough.” — From a crest to the next trough is half a wavelength; one wavelength is from a crest to the next crest.

9. VQ8 · Practice

Model answer. (a) The crests are at 0.2 m, 1.0 m and 1.8 m. One wavelength is the distance from one crest to the next: from 1.0 m to 1.8 m is 0.80 m. Across all three crests, (1.8 − 0.2) m ÷ 2 gaps gives the same 0.80 m. (b) The amplitude is measured from the rest line to a crest: 15 cm. From a trough at −15 cm to a crest at 15 cm is 30 cm, which is twice the amplitude.

Checked automatically

(a) Wavelength: 0.80 m (within ±0.02 m)
- Common wrong answer 0.53 : Count the gaps between the crests, not the crests: three crests have two gaps.
- Common wrong answer 1.6 : From the first crest to the third is two wavelengths: divide by 2.
- Common wrong answer 0.4 : From a crest to the next trough is only half a wavelength.
(b) Amplitude: 15 cm (within ±0.5 cm)
- Common wrong answer 30 : From a trough to a crest is twice the amplitude: measure from the rest line.

A full answer includes

(a) I found the distance from one crest to the next crest.
(a) I wrote 0.80 m.
(a) I did not use the distance from a crest to a trough (0.40 m).
(b) I measured from the rest line (0 cm) up to a crest (15 cm).
(b) I wrote 15 cm.
(b) I did not write 30 cm.

Also accept

(a) 0.80 m (b) 15 cm

Watch for

“Three crests means three wavelengths, so λ = 1.6 m ÷ 3.” — Count the gaps between the crests, not the crests: three crests have two gaps.
“The amplitude is 30 cm, from the bottom of a trough to the top of a crest.” — That is twice the amplitude. The amplitude is from the rest line to a crest.

10. VQ9 · Practice

Model answer. Change the wavelength to metres: 1.4 cm = 0.014 m. Then v = fλ = 15 Hz × 0.014 m = 0.21 m/s.

Checked automatically

Wave speed: 0.21 m/s (within ±0.005 m/s)
- Common wrong answer 21 : That is in cm/s: change 1.4 cm to metres first.
- Common wrong answer 11 : Multiply the frequency by the wavelength; do not divide.

A full answer includes

I changed 1.4 cm to 0.014 m.
I wrote v = fλ = 15 Hz × 0.014 m.
I wrote 0.21 m/s.
I did not give 21 as the answer in m/s.

Also accept

0.21 m/s

Watch for

“v = 15 × 1.4 = 21 m/s.” — That uses the wavelength in centimetres, so it gives the speed in cm/s. Change 1.4 cm to metres first.
“v = 15 ÷ 1.4 = 11 m/s.” — The wave speed is the frequency times the wavelength, not the frequency divided by it.

11. VQ10 · Practice

Model answer. From v = fλ, the wavelength is λ = v ÷ f = 1.3 m/s ÷ 1.2 Hz = 1.083… m, which is 1.1 m to 2 significant figures.

Checked automatically

Wavelength: 1.1 m (2 significant figures)
- Common wrong answer 1.6 : That is v × f; the wavelength is v ÷ f.
- Common wrong answer 0.92 : That is f ÷ v; the wavelength is v ÷ f.

A full answer includes

I rearranged v = fλ to λ = v ÷ f.
I wrote λ = 1.3 m/s ÷ 1.2 Hz.
I wrote 1.1 m, to 2 significant figures.
I did not multiply the speed by the frequency.

Also accept

1.1 m

Watch for

“λ = v × f = 1.6 m.” — Multiplying gives v × f, which is not a wavelength. Rearrange v = fλ: divide both sides by f.
“λ = f ÷ v = 0.92 m.” — That is upside down. Dividing both sides of v = fλ by f leaves λ = v ÷ f.

12. VQ11 · Practice

Model answer. The wavelength is the distance from one crest to the next, 9.0 m. From v = fλ, f = v ÷ λ = 3.6 m/s ÷ 9.0 m = 0.40 Hz: two waves pass every 5 seconds.

Checked automatically

Frequency: 0.40 Hz (within ±0.005 Hz)
- Common wrong answer 32 : That is v × λ; the frequency is v ÷ λ.
- Common wrong answer 2.5 : That is λ ÷ v, the time between waves in seconds; the frequency is v ÷ λ.

A full answer includes

I took the crest-to-crest distance, 9.0 m, as the wavelength.
I wrote f = v ÷ λ = 3.6 m/s ÷ 9.0 m.
I wrote 0.40 Hz.
I did not divide the wavelength by the speed.

Also accept

0.40 Hz

Watch for

“f = v × λ = 32 Hz.” — Rearrange v = fλ: divide both sides by λ.
“f = λ ÷ v = 2.5 Hz.” — That is upside down: 2.5 is the number of seconds between one wave and the next.

13. VQ12 · Practice

Model answer. Nine bright lines have eight gaps between them, so the distance from the first line to the ninth is eight wavelengths: divide it by 8. Measuring across eight wavelengths makes the small error in reading the ruler a much smaller part of the answer than measuring one wavelength, or half of one.

A full answer includes

I chose: measure from the first bright line to the ninth, and divide by 8.
I did not choose dividing by 9.

Also accept

measure from the first bright line to the ninth, and divide by 8

Watch for

“Measure from the first bright line to the ninth, and divide by 9.” — Nine lines have only eight gaps between them, so that distance is eight wavelengths, not nine.
“Measure from one bright line to the next, once, and use that.” — That does give one wavelength, but the error in reading the ruler is a large part of such a short distance.
“Measure from one bright line to the next dark line, and double it.” — That distance is only half a wavelength, so doubling it doubles the error in reading the ruler too.

14. VQ13 · Practice

Model answer. (a) The frequency is the number of vibrations each second: f = 27 ÷ 3.0 s = 9 Hz. (b) The amplitude is measured from the rest level to a crest, which is half the rise from a trough to a crest: 0.6 cm ÷ 2 = 0.3 cm. (c) A wavefront is a line along one crest, and from a crest to the next trough is half a wavelength, so λ = 2 × 0.8 cm = 1.6 cm. (d) The distance each crest travels in one second is the wave speed: v = fλ = 9 Hz × 1.6 cm = 14.4 cm/s, so 14.4 cm each second.

Checked automatically

(a) Frequency: 9 Hz (within ±0.1 Hz)
- Common wrong answer 81 : You multiplied the count by the time. The frequency is the count divided by the time.
- Common wrong answer 0.11 : That is 3.0 s ÷ 27, the time for one vibration. The frequency is the number of vibrations each second.
- Common wrong answer 27 : That is the number of vibrations in 3.0 s, not in one second.
(b) Amplitude: 0.3 cm (within ±0.02 cm)
- Common wrong answer 0.6 : That is the rise from a trough to a crest, twice the amplitude.
(c) Wavelength: 1.6 cm (within ±0.02 cm)
- Common wrong answer 0.8 : From a crest to the next trough is only half a wavelength.
(d) Distance each crest travels in one second: 14.4 cm (within ±0.5 cm)
- Common wrong answer 7.2 : That uses 0.8 cm, which is only half a wavelength.
- Common wrong answer 5.6 : That is f ÷ λ. The distance travelled each second is v = fλ.
- Common wrong answer 0.144 : That is in metres. Give the distance in centimetres.
- Common wrong answer 43 : That is 27 × 1.6 cm, the distance in 3.0 s. Use the number of waves in one second.

A full answer includes

(a) I divided the 27 vibrations by the 3.0 s.
(a) I wrote 9 Hz.
(b) I halved the 0.6 cm rise from a trough to a crest.
(b) I wrote 0.3 cm.
(b) I did not write 0.6 cm.
(c) I used that a wavefront is a line along a crest.
(c) I doubled the 0.8 cm from a crest to the next trough.
(c) I wrote 1.6 cm.
(c) I did not write 0.8 cm.
(d) I wrote v = fλ = 9 Hz × 1.6 cm.
(d) I wrote 14.4 cm.

Also accept

(a) 9 Hz (b) 0.3 cm (c) 1.6 cm (d) 14.4 cm

Watch for

“The amplitude is 0.6 cm, the rise from a trough to a crest.” — That is twice the amplitude. The amplitude is from the rest level to a crest.
“The wavelength is 0.8 cm, the distance from a wavefront to the next trough.” — A wavefront lies along a crest, and from a crest to the next trough is only half a wavelength.

15. VQ14 · Practice

Model answer. (a) From the first line to the sixth is 19.0 cm − 1.0 cm = 18.0 cm. Six lines have five gaps between them, so that is five wavelengths: λ = 18.0 cm ÷ 5 = 3.6 cm. (b) λ = v ÷ f. The speed stays the same and the frequency is twice as big, so the wavelength is half as long: 3.6 cm ÷ 2 = 1.8 cm. (c) The pupil counted the lines instead of the gaps between them. Six lines have only five wavelengths between them, so dividing by 6 gives a wavelength that is too short.

A full answer includes

(a) I took the 18.0 cm from the first line to the sixth.
(a) I divided it by 5, the number of gaps.
(a) I wrote 3.6 cm.
(a) I did not divide by 6.
(b) I used λ = v ÷ f with the same v and twice the f.
(b) I wrote 1.8 cm.
(b) I did not double the wavelength.
(c) I wrote that six lines have only five gaps between them.
(c) I wrote that 18.0 cm is five wavelengths, not six.

Also accept

(a) 3.6 cm (b) 1.8 cm (c) six lines have five gaps, not six

Watch for

“Six bright lines means six wavelengths.” — Each wavelength is a gap between two neighbouring lines, so six lines have five.
“A higher frequency gives a longer wavelength.” — At the same speed, λ = v ÷ f: more waves each second means each wave is shorter.

16. VT1 · Apply

Model answer. (a) The wavelength is 200 km = 200 000 m, so f = v ÷ λ = 200 m/s ÷ 200 000 m = 0.001 Hz: one wave passes every 1000 seconds, about 17 minutes. (b) The tsunami carries a huge amount of energy towards the coast, but not the water: each bit of water rises and falls about its own place, and the ship floating on it does the same. (c) The ship, like the water under it, vibrates up and down, while the wave travels horizontally. The direction of vibration is at right angles to the direction of propagation, and that is what a transverse wave is.

A full answer includes

(a) I changed 200 km to 200 000 m.
(a) I wrote f = v ÷ λ = 200 m/s ÷ 200 000 m.
(a) I wrote 0.001 Hz (one wave every 1000 s).
(a) I did not write 1000 Hz.
(b) I wrote that the wave transfers energy, not the water.
(b) I wrote that the ship moves up and down about the same place.
(b) I did not write that the tsunami pushes the water all the way to the coast.
(c) I wrote that the vibration (up and down) is at right angles to the direction of propagation (horizontal).

Also accept

(a) 0.001 Hz (b) energy, not water, is transferred; the ship moves up and down in place (c) vibration up and down, at right angles to the horizontal travel

Watch for

“The tsunami pushes a wall of water from the deep ocean all the way to the coast.” — Out at sea, each bit of water only rises and falls about its place; the energy is what travels to the coast.
“A frequency of 0.001 Hz means one wave every 0.001 s.” — Hertz counts waves each second. 0.001 waves each second is one wave every 1000 s.
“f = λ ÷ v = 1000 Hz.” — That is upside down: f = v ÷ λ. 1000 is the number of seconds between one wave and the next.