# Topic 4 &11 Review Waves & Oscillations

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1 Name: Date: Topic 4 &11 Review Waves & Oscillations 1. A source produces water waves of frequency 10 Hz. The graph shows the variation with horizontal position of the vertical displacement of the surface of water at one instant in time. vertical displacement / cm horizontal position / cm 0.4 The speed of the water waves is A cm s 1. B. 4.0 cm s 1. C. 10 cm s 1. D. 20 cm s Graph P shows how the displacement at one point in a wave varies with time. Graph Q shows how the displacement in the same wave varies with distance along the wave at one particular time. Graph P displacement 0 0 t 1 t 2 time Graph Q displacement 0 0 x 1 x x 2 3 distance 1

2 Which one of the following expressions gives the speed of the wave? A. B. C. D. x t x t ( x x ) 2 1 ( t t ) 2 1 ( x x ) 3 1 ( t t ) The two graphs show the variation with time of the individual displacements of two waves as they pass through the same point. The displacement of the resultant wave at the point at time T is equal to A. x 1 + x 2. B. x 1 x 2. C. A 1 + A 2. D. A 1 A 2. 2

3 4. The graph below shows the variation with time t of the displacement x of a particle undergoing simple harmonic motion. Which graph correctly shows the variation with time t of the acceleration a of the particle? 5. A wooden block is at rest on a horizontal frictionless surface. A horizontal spring is attached between the block and a rigid support. The block is displaced to the right by an amount X and is then released. The period of oscillations is T and the total energy of the system is E. X For an initial displacement of which of the following shows the best estimate for the period 2 of oscillations and the total energy of the system? Period A. T B. T C. D. T 2 T 2 Total energy E 2 E 4 E 2 E 4 3

4 6. Light travelling from water to air is incident on a boundary. Z Y X air water W Which of the following is a correct statement of Snell s law for this situation? A. sin Z = constant sin Y B. sin W = constant sin Z C. sin X = constant sin Z D. sin W = constant sin Y 7. Sound waves move faster in warm air than in cold air. The diagram below shows plane waves in cold air moving towards a boundary with warm air. warm air I II III cold air boundary IV Which of the arrows shows the possible direction of waves after reaching the boundary? A. I B. II C. III D. IV 4

5 8. Monochromatic light crosses the boundary between two media. Which of the following quantities is always the same for the light in both media? A. Amplitude B. Frequency C. Speed D. Wavelength 9. A sound emitting source moves along a straight line with speed v relative to an observer at rest. Observer v The speed of sound relative to the medium is c. The observer measures the speed of sound emitted by the source as A. c. B. c + v. C. c v. D. v c. 10. A source of sound emits waves of wavelength λ, period T and speed v when at rest. The source moves away from a stationary observer at speed V, relative to the observer. The wavelength of the sound waves, as measured by the observer is A. λ + vt. B. λ vt. C. λ +VT. D. λ VT. 5

6 11. Which one of the following diagrams best represents wavefronts produced by a source of sound of constant frequency as it moves at constant speed towards a stationary observer at O? A. B. O O C. D. O O 12. The waves from two light sources meet at a point. Which condition is essential for interference to be observed? A. Constant phase difference between the waves B. Equal amplitude of the waves C. Equal frequency of the waves D. Equal intensities of the waves 13. Two lamps producing light of the same colour are placed close to one another. A two source interference pattern is not observed because A. the lamps do not emit light of a single frequency. B. the phase difference between the light from the lamps is continually changing. C. the intensity of the light emitted by the lamps is not the same. D. the two lamps are not exact point sources. 6

7 14. Two identical sources in a ripple tank generate waves of wavelength λ. The interfering waves produce the wave pattern shown below. II III I IV Along which of the labelled lines is the path difference between the waves from the sources equal to 1.5 λ? A. I B. II C. III D. IV 15. A tube is filled with water and a vibrating tuning fork is held above its open end. x tuning fork y water tap The tap at the base of the tube is opened. As the water runs out, the sound is loudest when the water level is a distance x below the top of the tube. A second loud sound is heard when the water level is a distance y below the top. Which one of the following is a correct expression for the wavelength λ of the sound produced by the tuning fork? A. λ = y B. λ = 2x C. λ = y x D. λ = 2(y x) 7

8 16. Standing waves in an open pipe come about as a result of A. reflection and superposition. B. reflection and diffraction. C. superposition and diffraction. D. reflection and refraction. 17. A pipe, open at both ends, has a length L. The speed of sound in the air in the pipe is v. The frequency of vibration of the fundamental (first harmonic) standing wave that can be set up in the pipe is A. B. C. D. v 2 L. L 2 v. 4 v. L L 4 v. 18. A person is walking along one side of a building and a car is driving along another side of the building. The person can hear the car approach but cannot see it. This is explained by the fact that sound waves A. travel more slowly than light waves. B. are diffracted more at the corner of the building than light waves. C. are refracted more at the corner of the building than light waves. D. are longitudinal waves. 8

9 19. The diagram below shows ocean waves incident on a stone barrier protecting boats anchored behind it. Waves Boats Barrier The boats could still be at risk of damage by waves mainly as a result of A. refraction. B. standing waves. C. diffraction. D. reflection. 20. This question is about earthquake waves. (a) (i) Light is emitted from a candle flame. Explain why, in this situation, it is correct to refer to the speed of the emitted light, rather than its velocity (ii) By reference to displacement, describe the difference between a longitudinal wave and a transverse wave

10 The centre of an earthquake produces both longitudinal waves (P waves) and transverse waves (S waves). The graph below shows the variation with time t of the distance d moved by the two types of wave. d / km 1200 P wave S wave t / s (b) Use the graph to determine the speed of (i) the P waves (ii) the S waves The waves from an earthquake close to the Earth s surface are detected at three laboratories L 1, L 2 and L 3. The laboratories are at the corners of a triangle so that each is separated from the others by a distance of 900 km, as shown in the diagram below. L 900 km 1 2 L L 3 10

11 The records of the variation with time of the vibrations produced by the earthquake as detected at the three laboratories are shown below. All three records were started at the same time. L 1 L 2 start of trace time L 3 On each record, one pulse is made by the S wave and the other by the P wave. The separation of the two pulses is referred to as the S-P interval. (c) (i) On the trace produced by laboratory L 2, identify, by reference to your answers in (b), the pulse due to the P wave (label the pulse P). (ii) Using evidence from the records of the earthquake, state which laboratory was closest to the site of the earthquake... (iii) State three separate pieces of evidence for your statement in (c)(ii) (iv) The S-P intervals are 68 s, 42 s and 27 s for laboratories L 1, L 2 and L 3 respectively. Use the graph, or otherwise, to determine the distance of the earthquake from each laboratory. Explain your working. Distance from L 1 =...km.. Distance from L 2 =...km.. Distance from L 3 =...km (v).. Mark on the diagram a possible site of the earthquake. (4) 11

12 There is a tall building near to the site of the earthquake, as illustrated below. building ground direction of vibrations The base of the building vibrates horizontally due to the earthquake. (d) (i) On the diagram, draw the fundamental mode of vibration of the building caused by these vibrations. The building is of height 280 m and the mean speed of waves in the structure of the building is ms 1. (ii) Explain quantitatively why earthquake waves of frequency about 6 Hz are likely to be very destructive (Total 21 marks) 21. This question is about the interference of waves. (a) State the principle of superposition

13 A wire is stretched between two points A and B. A B A standing wave is set up in the wire. This wave can be thought of as being made up from the superposition of two waves, a wave X travelling from A to B and a wave Y travelling from B to A. At one particular instant in time, the displacement of the wire is as shown. A background grid is given for reference and the equilibrium position of the wire is shown as a dotted line. A B (b) On the grids below, draw the displacement of the wire due to wave X and wave Y. Wave X A B Wave Y A B (4) 13

14 The diagram below shows an arrangement (not to scale) for observing the interference pattern produced by the superposition of two light waves. P S 1 monochromatic light source S O S 2 single slit double slit Screen S 1 and S 2 are two very narrow slits. The single slit S ensures that the light leaving the slits S 1 and S 2 is coherent. (c) (i) Define coherent..... (ii) Explain why the slits S 1 and S 2 need to be very narrow (Total 9 marks) 14

15 22. Waves on a string A travelling wave is created on a string. The graph below shows the variation with time t of the displacement y of a particular point on the string. Graph 1 y / mm t / ms The variation with distance x of the displacement y of the string at t = 0 is shown below. Graph 2 y / mm x / cm (a) Use information from the graphs to calculate, for this wave, (i) the wavelength; (ii) the frequency; (iii) the speed of the wave. (b) The wave is moving from left to right and has period T. (i) On graph 1, draw a labelled line to indicate the amplitude of the wave. T (ii) On graph 2, draw the displacement of the string at t =. 4 15

16 (c) One end of the string is attached to a wall. A student creates a single pulse in the string that travels to the right as shown in the diagram below. string pulse wall (i) In the space below, draw a diagram to show the shape and size of the pulse after it has been reflected from the wall. (ii) By reference to Newton s third law, explain the nature of the reflected pulse that you have drawn in (c)(i) above. (d) The free end of the string in (c) is now made to oscillate with frequency f such that a standing wave is established on the string. The diagram below illustrates the standing wave. wall free end 16

17 (i) Explain, by reference to the principle of superposition, the formation of a standing wave. (ii) The length of the string is 3.0 m. Using your answer for the speed of the wave in (a)(iii) calculate the frequency f. (e) A satellite orbits the Earth at a fixed height above the equator. Two coherent radio transmitters on the equator emit radio waves of equal amplitude as illustrated in the diagram below. satellite orbit satellite Earth radio transmitters not to scale The signal that the satellite receives varies in intensity. (i) State what is meant by coherent sources. 17

18 (ii) Suggest why the signal received by the satellite varies in intensity. (iii) The transmitters have a separation of 160 m and emit waves of wavelength 1.2 m. The signal received by the satellite varies in intensity with a frequency of 3.0 Hz as it flies overhead. The speed of the satellite is 7.7 km s 1. Calculate the height of the satellite above the Earth s surface. (Total 22 marks) 23. Simple harmonic motion and the greenhouse effect (a) A body is displaced from equilibrium. State the two conditions necessary for the body to execute simple harmonic motion

19 (b) In a simple model of a methane molecule, a hydrogen atom and the carbon atom can be regarded as two masses attached by a spring. A hydrogen atom is much less massive than the carbon atom such that any displacement of the carbon atom may be ignored. The graph below shows the variation with time t of the displacement x from its equilibrium position of a hydrogen atom in a molecule of methane. The mass of hydrogen atom is kg. Use data from the graph above (i) to determine its amplitude of oscillation. (ii) to show that the frequency of its oscillation is Hz. (iii) to show that the maximum kinetic energy of the hydrogen atom is J. 19

20 (c) Assuming that the motion of the hydrogen atom is simple harmonic, its frequency of oscillation f is given by the expression f = 1 2π k m p, where k is the force per unit displacement between a hydrogen atom and the carbon atom and m p is the mass of a proton. (i) Show that the value of k is approximately 560 N m 1. (ii) Estimate, using your answer to (c)(i), the maximum acceleration of the hydrogen atom. (d) Methane is classified as a greenhouse gas. (i) Describe what is meant by a greenhouse gas. (ii) Electromagnetic radiation of frequency Hz is in the infrared region of the electromagnetic spectrum. Suggest, based on the information given in (b)(ii), why methane is classified as a greenhouse gas. (Total 14 marks) 20

21 24. This question is about sound waves Production of sound waves (a) Distinguish, in terms of the propagation of energy, the difference between a transverse travelling wave and a longitudinal travelling wave (b) The diagram below shows an aluminium rod AB of length 1.50 m hanging horizontally from two strings. string string hammer A 1.50 m B aluminium rod End A of the rod is hit gently with a hammer. As a result, a wave pulse travels down the rod and is reflected from end B. The hammer remains in contact with the rod until the pulse reflected from end B reaches A. This pulse causes the hammer to rebound from the end of the rod. (i) Suggest, giving a reason, whether the wave pulse is longitudinal or transverse. (ii) The hammer is in contact with end A of the rod for s. Calculate the speed of the pulse in the rod. 21

22 (iii) As a result of the rod being hit with the hammer, a sound is heard. Suggest how this sound arises. (iv) The sound produced in the air consists of waves of many different frequencies and intensities. The loudest sound corresponds to a wave of frequency Hz. Deduce that this frequency is due to the rod vibrating in its fundamental (first harmonic) mode. Interference of sound waves (c) In the diagram below, S 1 and S 2 are two small loudspeakers. They are connected to the same sound source such that they emit sound waves of the same intensity and wavelength. An instrument for detecting sound intensity is placed at point P such that S 1 P = S 2 P. X S 1 P S 2 The speaker S 1 is moved slowly away from P along the line PS 1. As S 1 is moved, the sound detected at P decreases and increases in intensity. (i) Explain this observation. 22

23 (ii) In moving the source from S 1 to point X, the intensity of the sound at P changes from a maximum to a minimum. The distance S 1 X = m. Calculate the value of the wavelength of the sound emitted by the sources. (iii) S 1 remains at the point X and the frequency f of the sound emitted from both S 1 and S 2 is changed until a maximum of sound intensity is detected at P. This occurs when f = 4100 Hz. Estimate a value for the speed of sound. (Total 20 marks) 23

24 25. This question is about the Doppler effect. The diagram below shows wavefronts produced by a stationary wave source S. The spacing of the wavefronts is equal to the wavelength of the waves. The wavefronts travel with speed V. S (a) The source S now moves to the right with speed 2 1 V. In the space below, draw four successive wavefronts to show the pattern of waves produced by the moving source. (b) Derive the Doppler formula for the observed frequency f 0 of a sound source, as heard by a stationary observer, when the source approaches the stationary observer with speed v. The speed of sound is V and the frequency of the sound emitted by the source is f

25 The Sun rotates about its centre. The light from one edge of the Sun, as seen by a stationary observer, shows a Doppler shift of nm for light of wavelength nm. (c) Assuming that the Doppler formula for sound may be used for light, estimate the linear speed of a point on the surface of the Sun due to its rotation (Total 9 marks) 26. The properties of sound waves Reflection and Refraction One method of finding the position of fish beneath a boat is to send out a pulse of sound waves from the bottom of a boat and time how long the pulse takes to return as shown below. The speed of sound waves in water is 1500 m s 1. emitter and receiver water fish (a) The time between the pulse leaving the emitter and returning to the receiver is 12 ms. Calculate the distance from the bottom of the boat to the fish

26 In order to find fish using this method, the effects of diffraction at the fish need to be minimized. (b) (i) The diagram below shows plane wavefronts incident on an obstacle. Complete the diagram to show what is meant by diffraction of the wavefronts. direction of movement of wavefronts (ii) Explain why you would expect the effects of diffraction to be negligible when sound of frequency 60 khz is incident on a large fish. The Doppler effect can be used to determine the speed of an object. (c) (i) Explain what is meant by the Doppler effect. (ii) A train approaches and then passes by a stationary observer. The train is moving with constant velocity and emits a sound of constant frequency. The observer hears the frequency change from 490 Hz to 410 Hz. The speed of sound in air is 340 m s 1. Estimate the speed of the train. (4) (Total 12 marks) 26

27 27. This question is about single slit diffraction. The diagram below shows an experimental arrangement for observing Fraunhofer diffraction by a single slit. After passing through the convex lens L 1, monochromatic light from a point source P is incident on a narrow, rectangular single slit. After passing through the slit the light is brought to a focus on the screen by the lens L 2. The point source P is at the focal point of the lens L 1. P X L L 1 2 single slit screen The point X on the screen is directly opposite the central point of the slit. (a) Explain qualitatively how Huygens principle accounts for the phenomenon of single slit diffraction (b)... Using the axes below draw a graph to show how the intensity of the pattern varies with distance along the screen. The point X on the screen is shown as a reference point. (This is a sketch graph; you do not need to add any numerical values.) intensity X distance along screen 27

28 (c) In this experiment the light has a wavelength of 500 nm and the width of the central maximum of intensity on the screen is 10.0 mm. When light of unknown wavelength λ is used, the width of the central maximum of intensity is 13.0 mm. Determine the value of λ The lens L 1 is now removed and another point source Q emitting light of the same wavelength as P (500 nm) is placed 5.0 mm from P and the two sources are arranged as shown below. P 5.0 mm Q 1.50 m b Single slit The distance between the sources and the slit is 1.50 m. (d) (i) State the condition for the image of P and the image of Q formed on the screen to be just resolved..... (ii) Determine the minimum width b of the slit for the two images to be just resolved (Total 10 marks) 28

29 28. This question is about resolution. (a) State the name of the wave phenomenon that limits the resolution of any optical instrument (b) Explain with the aid of a diagram, the Rayleigh criterion (Total 4 marks) 29. This question is about optical resolution. (a) Light from a point source is brought to a focus by a convex lens. The lens does not cause spherical or chromatic aberration. (i) State why the image of the point source will not be a point image..... (ii) Describe the appearance of the image

30 Two light receptors at the back of the eye are 4.0 µm apart. The distance of the receptors from the convex lens at the front of the eye is 17.0 mm, as shown below. eye lens light receptor α 4.0 µ m 17.0 mm Light of wavelength 550 nm from two point objects enters the eye. The centres of the images of the two objects are focused on the light receptors. (b) (i) Calculate the angle α in radians subtended by the two receptors at the centre of the eye lens..... (ii) Use the Rayleigh criterion to calculate the diameter of the pupil of the eye so that the two images are just resolved..... (Total 7 marks) 30. A student uses a diffraction grating to view the visible part of the sodium emission spectrum. (a) Explain how the diffraction grating is able to separate light into component wavelengths (b) Sodium light is incident normally on a grating having 6000 lines per centimetre. Calculate the angle at which light of wavelength nm will be seen in the first order spectrum (Total 5 marks) 30

31 31. This question is about diffraction and resolution. Blue light of wavelength 450 nm from a star passes through a telescope with a circular aperture of 0.25 m and forms an image on a photographic plate 0.75 m from the focussing lens. (a) (i) In the space provided below, draw a labelled sketch to show the diffraction fringe pattern produced on the photographic plate. (ii) Calculate the diameter of the central maximum on the photographic plate. (b) The telescope in (a) is now pointed at two stars. The maximum separation of the stars is d and they are both m from the telescope. (i) Determine the separation d of the stars such that the images of the stars are just resolved in light of wavelength 450 nm. 31

32 (ii) Over a period of time the separation of the stars varies from 2 d to 2d. Describe and explain the changes to the image produced by the telescope during this time. You should include diagrams to illustrate your answer. (Total 10 marks) 32

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