Waves (GCSE Science) - Worksheets, Questions and Revision

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GCSE · Physics

P6 Waves

AQA 8463 · Calculator allowed · about 80 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Waves can be described as either transverse or longitudinal.

(a)Define a transverse wave and give one example of a transverse wave.(2)

(b)Define a longitudinal wave and give one example of a longitudinal wave.(2)

(Total for Question 1 is 4 marks)

A transverse wave is drawn on a diagram showing an undisturbed (equilibrium) line running through the middle of the wave. The vertical distance from the undisturbed line up to the peak of the wave is labelled X. The horizontal distance between two adjacent peaks is labelled Y.

Figure (to be drawn): A transverse wave drawn about a horizontal undisturbed (equilibrium) line. X is the vertical distance from the undisturbed line to the top of a peak. Y is the horizontal distance between the tops of two adjacent peaks.

(a)Which label, X or Y, shows the amplitude of the wave?(1)

(b)Which label, X or Y, shows the wavelength of the wave?(1)

(c)State the SI unit used to measure wavelength.(1)

(Total for Question 2 is 3 marks)

A loudspeaker cone vibrates 500 times each second, producing a sound wave.

(a)State what is meant by the frequency of a wave.(1)

(b)Calculate the period of the sound wave produced by the loudspeaker. Use the Physics Equations Sheet: T = 1 / f(2)

(Total for Question 3 is 3 marks)

A water wave travelling across a pond has a wavelength of 0.4 m and a frequency of 5 Hz.

(a)Write down the word equation linking wave speed, frequency and wavelength.(1)

(b)Calculate the speed of the wave. Use the Physics Equations Sheet: wave speed = frequency x wavelength(2)

(Total for Question 4 is 3 marks)

A sound wave travels through air at a speed of 340 m/s and has a frequency of 850 Hz.

(a)Rearrange the wave speed equation, wave speed = frequency x wavelength, to make wavelength the subject.(1)

(b)Calculate the wavelength of the sound wave. Use the Physics Equations Sheet: wave speed = frequency x wavelength(2)

(Total for Question 5 is 3 marks)

Required practical: Priya investigates the speed of water waves using a ripple tank. She uses a stroboscope to find that the dipper is producing waves at a frequency of 4 Hz. She then measures the distance across 5 complete waves on the water surface and finds it to be 60 cm.

(a)Explain why measuring the distance across 5 complete waves, rather than measuring a single wavelength, gives a more accurate value for the wavelength.(2)

(b)Calculate the wavelength of one wave.(2)

(c)Calculate the speed of the water waves. Use the Physics Equations Sheet: wave speed = frequency x wavelength(2)

(Total for Question 6 is 6 marks)

Required practical: Tom uses a signal generator, a loudspeaker and an oscilloscope to investigate a sound wave travelling through a steel rod. On the oscilloscope screen, one complete wave takes up 4 divisions, and each division represents 0.5 ms.

Figure (to be drawn): An oscilloscope trace showing a repeating sine wave. One complete cycle spans 4 horizontal divisions on the screen grid; each division represents 0.5 ms on the time base.

(a)Calculate the time period of the wave shown on the oscilloscope, in seconds.(2)

(b)Calculate the frequency of the sound wave. Use the Physics Equations Sheet: T = 1 / f(2)

(c)The wavelength of the sound wave in the steel rod is 10.3 m. Calculate the speed of sound in the steel rod. Use the Physics Equations Sheet: wave speed = frequency x wavelength(2)

(Total for Question 7 is 6 marks)

Here are five types of electromagnetic wave, listed in a jumbled order: visible light, γ rays, microwaves, ultraviolet, radio waves. Write the five waves in order of increasing frequency, starting with the lowest frequency.

(Total for Question 8 is 4 marks)

For each of the following types of electromagnetic wave, state one everyday use and one associated hazard: (i) microwaves (ii) infrared (iii) ultraviolet (iv) X-rays (v) γ rays.

(Total for Question 9 is 5 marks)

Explain why γ rays are much more hazardous to human tissue than radio waves.

(Total for Question 10 is 3 marks)

A ray of light strikes a plane mirror.

Figure (to be drawn): A ray of light striking a plane mirror, meeting the mirror surface at 35 degrees measured along the mirror surface itself.

(a)State the law of reflection.(1)

(b)A ray of light hits the mirror surface at an angle of 35 degrees, measured from the mirror surface (not the normal). Calculate the angle of reflection, measured from the normal.(2)

(Total for Question 11 is 3 marks)

A ray of light travels from air into a glass block, hitting the boundary at an angle (not along the normal).

Figure (to be drawn): A ray of light travelling from air into a glass block, hitting the flat boundary at an angle to the normal (a dashed line drawn perpendicular to the boundary at the point of incidence).

(a)State what happens to the speed of the light wave as it passes from air into the glass block.(1)

(b)Explain, in terms of the wavefronts, why this change in speed causes the ray of light to bend towards the normal as it enters the glass block.(3)

(Total for Question 12 is 4 marks)

A smooth bathroom mirror produces a clear, sharp reflection of a person's face, but a sheet of white paper reflects light without producing any clear image.

(a)State what is meant by specular reflection.(1)

(b)Explain why light reflecting off the rough surface of the paper does not produce a clear image.(2)

(Total for Question 13 is 3 marks)

An object is placed further from a converging lens than the lens's 2F point (twice the focal length).

Figure (to be drawn): A ray diagram for a converging lens: an object placed beyond the 2F point on the left of the lens, with the principal axis, F and 2F points marked on both sides.

(a)State whether the image formed by the lens is real or virtual.(1)

(b)Describe two other properties of the image formed.(2)

(Total for Question 14 is 3 marks)

A converging lens is used to form an image of an object.

(a)An object of height 2 cm produces an image of height 0.5 cm. Calculate the magnification produced by the lens. Use the Physics Equations Sheet: magnification = image height / object height(2)

(b)A second lens produces a magnification of 3 for an object of height 1.5 cm. Calculate the height of the image formed.(2)

(Total for Question 15 is 4 marks)

Required practical: A student investigates the speed of water waves in a ripple tank. She changes the frequency of the dipper and measures the resulting wavelength of the waves produced each time, in order to test whether her results agree with the equation wave speed = frequency x wavelength. Evaluate this method. Your answer should include how the student could improve the accuracy and reliability of her wavelength measurements, and how she could use her results to check whether they support the equation.

(Total for Question 16 is 6 marks)

The human ear can only detect sound waves within a limited range of frequencies.

(a)State the approximate range of frequencies that a healthy human ear can hear.(1)

(b)Bats use ultrasound (sound waves above the range of human hearing) with a much shorter wavelength than typical audible sound to detect small insects in flight. Suggest why using a shorter-wavelength sound wave allows the bat to detect smaller objects.(2)

(Total for Question 17 is 3 marks)

Aisha wants to measure the speed of sound in air. She stands 170 m from a large flat wall, claps her hands once and starts a stopwatch at the same instant. She stops the stopwatch as soon as she hears the echo. The stopwatch reads 1.0 s.

(a)Calculate the speed of sound in air using Aisha's results. Use the Physics Equations Sheet: speed = distance / time(2)

(b)The sound wave produced by the clap has a frequency of 340 Hz. Using your answer to part a) and the wave speed equation, calculate the wavelength of the sound wave.(3)

(Total for Question 18 is 5 marks)

A student uses a ripple tank to test the equation wave speed = frequency x wavelength, by measuring the wavelength produced at several different dipper frequencies. Her results are: frequency = 2 Hz, wavelength = 40 cm; frequency = 4 Hz, wavelength = 20 cm; frequency = 6 Hz, wavelength = 20 cm; frequency = 8 Hz, wavelength = 10 cm; frequency = 10 Hz, wavelength = 8 cm.

Figure (to be drawn): A table of results: frequency in Hz (2, 4, 6, 8, 10) against measured wavelength in cm (40, 20, 20, 10, 8).

(a)For the results at 2 Hz, 4 Hz, 8 Hz and 10 Hz, calculate the speed of the wave in each case (convert each wavelength to metres first), and show that the wave speed is approximately constant for these four results.(3)

(b)Identify which one of the five results is anomalous, and calculate the wavelength that would have been expected at that frequency for consistency with the rest of the data.(3)

(Total for Question 19 is 6 marks)

Mark scheme · P6 Waves

Question 1

(a) B1 a wave in which the oscillations (vibrations) are at right angles (perpendicular) to the direction of energy transfer, oe
(a) B1 correct example, e.g. light/electromagnetic waves/ripples on water/waves on a rope
(a) Answer: A transverse wave has oscillations at right angles to the direction of energy transfer, e.g. light waves.
(b) B1 a wave in which the oscillations are parallel to (along) the direction of energy transfer, oe
(b) B1 correct example, e.g. sound waves/P-waves (seismic waves)/waves on a slinky spring
(b) Answer: A longitudinal wave has oscillations parallel to the direction of energy transfer, e.g. sound waves.

Question 2

(a) B1 X
(a) Answer: X
(b) B1 Y
(b) Answer: Y
(c) B1 metre, m
(c) Answer: Metre (m)

Question 3

(a) B1 the number of complete waves (oscillations) passing a point per second, oe
(a) Answer: The number of complete waves passing a point each second.
(b) M1 substitution: T = 1 / 500
(b) A1 T = 0.002 s (2 x 10^-3 s), cao, with unit
(b) Answer: T = 0.002 s

Question 4

(a) B1 wave speed = frequency x wavelength
(a) Answer: wave speed = frequency x wavelength
(b) M1 substitution: v = 5 x 0.4
(b) A1 v = 2 m/s, cao, with unit
(b) Answer: v = 2 m/s

Question 5

(a) B1 wavelength = wave speed / frequency
(a) Answer: wavelength = wave speed / frequency
(b) M1 substitution: wavelength = 340 / 850
(b) A1 wavelength = 0.4 m, cao, with unit
(b) Answer: wavelength = 0.4 m

Question 6

(a) B1 reduces the percentage (relative) error/uncertainty in the measurement
(a) B1 because the same absolute reading error (e.g. from the ruler) is spread over a much longer measured distance, oe
(a) Answer: Measuring across several wavelengths reduces the percentage error, because any reading error is a smaller fraction of a longer distance.
(b) M1 60 / 5 = 12 (cm)
(b) A1 wavelength = 0.12 m, cao, with unit converted to metres
(b) Answer: wavelength = 0.12 m
(c) M1 substitution: v = 4 x 0.12
(c) A1 v = 0.48 m/s, cao, with unit
(c) Answer: v = 0.48 m/s

Question 7

(a) M1 4 x 0.5 = 2 (ms)
(a) A1 T = 0.002 s (2 x 10^-3 s), cao, with unit
(a) Answer: T = 0.002 s
(b) M1 rearrange and substitute: f = 1 / 0.002
(b) A1 f = 500 Hz, cao, with unit
(b) Answer: f = 500 Hz
(c) M1 substitution: v = 500 x 10.3
(c) A1 v = 5150 m/s, cao, with unit
(c) Answer: v = 5150 m/s

Question 8

B1 radio waves placed before microwaves
B1 microwaves placed before visible light
B1 visible light placed before ultraviolet
B1 ultraviolet placed before γ rays
Answer: radio waves, microwaves, visible light, ultraviolet, γ rays (lowest to highest frequency)

Question 9

B1 microwaves: use e.g. satellite communications/cooking food; hazard = internal heating of body tissue/cells
B1 infrared: use e.g. cooking, thermal imaging, remote controls; hazard = skin burns
B1 ultraviolet: use e.g. sun tanning, fluorescent lamps, security marking; hazard = skin cancer/skin ageing/eye damage
B1 X-rays: use e.g. medical imaging of bones, airport security scanning; hazard = mutation of cells/cancer risk
B1 γ rays: use e.g. sterilising medical equipment, treating cancer (radiotherapy); hazard = cancer/cell mutation/cell death
Answer: See mark scheme for accepted use-hazard pairs for each wave type.

Question 10

B1 γ rays have a much higher frequency (and therefore carry more energy per photon) than radio waves
B1 γ rays are ionising and can remove electrons from atoms/damage or mutate DNA in cells, which can cause cancer
B1 radio waves are non-ionising / do not carry enough energy to remove electrons or damage cells, so are essentially harmless at normal exposure
Answer: Gamma rays have much higher frequency and energy than radio waves, so are ionising and can damage DNA in cells, causing cancer; radio waves are non-ionising and do not have enough energy to cause this damage.

Question 11

(a) B1 the angle of incidence equals the angle of reflection (both measured from the normal), oe
(a) Answer: The angle of incidence equals the angle of reflection.
(b) M1 angle of incidence (from the normal) = 90 - 35 = 55 (degrees)
(b) A1 angle of reflection = 55 degrees, cao, since angle of reflection = angle of incidence
(b) Answer: 55 degrees

Question 12

(a) B1 the speed of the light wave decreases, since glass is a denser (optically denser) medium than air
(a) Answer: The speed decreases.
(b) B1 one side of the wavefront reaches the boundary and slows down before the rest of the wavefront, which is still travelling faster in the air
(b) B1 this causes the wavefront (and therefore the direction of travel of the wave) to change direction/pivot at the boundary
(b) B1 the ray bends towards the normal because it is entering a denser medium in which the wave travels more slowly
(b) Answer: The part of the wavefront reaching the glass first slows down while the rest keeps moving faster in air, turning the wavefront and bending the ray towards the normal.

Question 13

(a) B1 reflection from a smooth surface in which parallel incident rays are all reflected in a single direction (parallel rays remain parallel), oe
(a) Answer: Reflection from a smooth surface where parallel rays are all reflected in the same direction.
(b) B1 the paper's surface is rough/uneven at a small scale, so the normal at each point on the surface faces a different direction
(b) B1 parallel incident rays are therefore reflected in many different directions (diffuse reflection), so no consistent image can form
(b) Answer: The rough surface has normals pointing in many directions, so parallel light rays are scattered (diffuse reflection) rather than reflected in one direction, preventing a clear image forming.

Question 14

(a) B1 real
(a) Answer: Real
(b) B1 the image is inverted (upside down)
(b) B1 the image is diminished (smaller than the object), formed between F and 2F on the other side of the lens
(b) Answer: Inverted and diminished (smaller than the object).

Question 15

(a) M1 substitution: magnification = 0.5 / 2
(a) A1 magnification = 0.25, cao (no unit, magnification has no units)
(a) Answer: magnification = 0.25
(b) M1 rearrange and substitute: image height = 3 x 1.5
(b) A1 image height = 4.5 cm, cao, with unit
(b) Answer: image height = 4.5 cm

Question 16

Level 1 (1-2): A simple, isolated statement (or statements) is made about the method or a possible improvement, with little or no reasoning or linkage to accuracy or reliability.
Level 2 (3-4): Relevant improvements to the method are described, with some linkage of ideas showing how the changes would improve the accuracy or reliability of the results.
Level 3 (5-6): A detailed and coherent evaluation is given, covering both how to improve the accuracy/reliability of the wavelength and frequency measurements and how to check whether the results support wave speed = frequency x wavelength, with clear scientific reasoning throughout.
Indicative content:
- Use a stroboscope to make the moving wave pattern appear stationary, allowing the wavelength to be measured more accurately.
- Measure the distance across several complete waves (e.g. 5 or 10) and divide by the number of waves, to reduce the percentage error in the wavelength measurement.
- Take repeat readings at each frequency and calculate a mean wavelength, to improve reliability and help identify anomalous results.
- Keep the depth of water in the tank constant (control variable), since wave speed depends on water depth, so changing the depth would make it an unfair test.
- View the wave pattern from directly above and use a fixed marker or set square to avoid parallax error when measuring.
- Calculate the wave speed (wave speed = frequency x wavelength) for each frequency tested; if the equation holds, the calculated speed should stay approximately constant across all frequencies, since wave speed depends on water depth, not frequency.
- Plot a graph of wavelength against 1/frequency; a straight line through the origin would support wave speed = frequency x wavelength, with the gradient equal to the wave speed.
- Repeat the whole experiment and compare results, re-testing any anomalous points that do not fit the overall pattern.

Question 17

(a) B1 approximately 20 Hz to 20 000 Hz (20 kHz)
(a) Answer: 20 Hz to 20 000 Hz
(b) B1 waves diffract (spread out) around obstacles/gaps that are similar in size to their wavelength; a longer-wavelength wave would diffract around a small insect rather than reflecting off it
(b) B1 the shorter-wavelength ultrasound is closer in size to (or smaller than) the insect, so it reflects off the insect and produces a detectable echo instead of diffracting around it
(b) Answer: Shorter-wavelength ultrasound diffracts less around a small insect than longer-wavelength sound would, so it reflects off the insect and produces an echo the bat can detect.

Question 18

(a) M1 total distance travelled by the sound = 2 x 170 = 340 (m), since the sound travels to the wall and back
(a) A1 speed = 340 / 1.0 = 340 m/s, cao, with unit
(a) Answer: speed of sound = 340 m/s
(b) M1 select and rearrange wave speed = frequency x wavelength to give wavelength = wave speed / frequency
(b) M1 substitute the speed found in part a): wavelength = 340 / 340
(b) A1 wavelength = 1.0 m, cao, with unit
(b) Answer: wavelength = 1.0 m

Question 19

(a) M1 correct unit conversion of wavelength to metres for at least two results (e.g. 40 cm = 0.40 m)
(a) M1 correct use of wave speed = frequency x wavelength for at least three of the four results, e.g. 2 x 0.40 = 0.8 m/s; 4 x 0.20 = 0.8 m/s; 8 x 0.10 = 0.8 m/s; 10 x 0.08 = 0.8 m/s
(a) A1 conclusion that the wave speed is approximately constant at about 0.8 m/s for these four results, cso
(a) Answer: The wave speed is approximately constant at 0.8 m/s for the 2 Hz, 4 Hz, 8 Hz and 10 Hz results.
(b) B1 the 6 Hz result (wavelength = 20 cm) is anomalous
(b) M1 use the constant wave speed of 0.8 m/s found in part a) with wavelength = wave speed / frequency = 0.8 / 6
(b) A1 expected wavelength = 0.13 m (13.3 cm, 2 s.f.), cao, awrt 0.13 m
(b) Answer: The 6 Hz result is anomalous; the expected wavelength would be about 0.13 m (13.3 cm), not the recorded 20 cm.

Question 19

6 marks

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Waves (GCSE Science) - Worksheets, Questions and Revision

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Question 19

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