2. The graph shows how the displacement varies with time for an object undergoing simple harmonic motion.

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1 Practice Test: 29 marks (37 minutes) Additional Problem: 31 marks (45 minutes) 1. A transverse wave travels from left to right. The diagram on the right shows how, at a particular instant of time, the displacement of particles in the medium varies with position. Which arrow represents the direction of the velocity of the particle marked P? 2. The graph shows how the displacement varies with time for an object undergoing simple harmonic motion. Which graph shows how the object s acceleration a varies with time t? 1/12

2 3. Which of the following is a value of wavelength that is found in the visible region of the electromagnetic spectrum? A m C m B m D m 4. The shock absorbers of a car, in good working condition, ensure that the vertical oscillations of the car are A. undamped. B. lightly damped. C. moderately damped. D. critically damped. 5. The graphs show how the acceleration a of four different particles varies with their displacement x. Which of the particles is executing simple harmonic motion? 2/12

3 6. The diagram on the right is a snapshot of wave fronts of circular waves emitted by a point source S at the surface of water. The source vibrates at a frequency f = 10.0 Hz. The speed of the wave front is A cm s 1. B. 1.5 cm s 1. C. 15 cm s 1. D. 30 cm s Two coherent point sources S 1 and S 2 emit spherical waves. Which of the following best describes the intensity of the waves at P and Q? P Q A. maximum minimum B. minimum maximum C. maximum maximum D. minimum minimum 3/12

4 8. An object at the end of a spring oscillates vertically with simple harmonic motion. The graph shows the variation with time t of the displacement x. The amplitude is x 0 and the period of oscillation is T. Which of the following is the correct expression for the displacement x? 2 A. x0 cos t C. T x 0 2 sin t T 2 B. x cos t D. T 2 T 0 x0 sin t 9. A mass on the end of a horizontal spring is displaced from its equilibrium position by a distance A and released. Its subsequent oscillations have total energy E and time period T. An identical mass is attached to an identical spring. The maximum displacement is 2A. Assuming this spring obeys Hooke s law, which of the following gives the correct time period and total energy? New time period New energy A. T 4E B. T 2E C. 2T 4E D. 2T 2E 4/12

5 10. What is the best estimate for the refractive index of a medium in which light travels at a speed of m s 1? A. 0.9 B. 1.0 C. 1.1 D Plane wavefronts are incident on a boundary between two media labelled 1 and 2 in the diagram. The diagram of the wavefronts is drawn to scale. The ratio of the refractive index of medium 2 to that of medium 1 is A B C D An orchestra playing on boat X can be heard by tourists on boat Y, which is situated out of sight of boat X around a headland. The sound from X can be heard on Y due to A. refraction. B. reflection. C. diffraction. D. transmission. 5/12

6 13. Which of the following correctly describes the change, if any, in the speed, wavelength and frequency of a light wave as it passes from air into glass? Speed Wavelength Frequency A. decreases decreases unchanged B. decreases unchanged decreases C. unchanged increases decreases D. increases increases unchanged 14. A sound wave of frequency 660 Hz passes through air. The variation of particle displacement with distance along the wave at one instant of time is shown below. 0.5 displacement / mm distance / m 0.5 (a) (b) State whether this wave is an example of a longitudinal or a transverse wave.... Using data from the above graph, deduce for this sound wave, (i) the wavelength... the amplitude... (iii) the speed..... (Total 5 marks) 6/12

7 15. Travelling waves (a) Graph 1 below shows the variation with time t of the displacement d of a travelling (progressive) wave. Graph 2 shows the variation with distance x along the same wave of its displacement d. Graph 1 d / mm t / s 4 Graph 2 d / mm x / cm 4 (i) State what is meant by a travelling wave. Use the graphs to determine the amplitude, wavelength, frequency and speed of the wave. Amplitude:... Wavelength:... Frequency: Speed: /12

8 Refraction of waves (b) The diagram below shows plane wavefronts incident on a boundary between two media A and B. medium A medium B The ratio refractive index of medium B is1.4. refractive index of medium A The angle between an incident wavefront and the normal to the boundary is 50. (i) Calculate the angle between a refracted wavefront and the normal to the boundary. (3) On the diagram above, construct three wavefronts to show the refraction of the wave at the boundary. (3) (Total 11 marks) Additional problems 16. 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 /12

9 (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. to show that the frequency of its oscillation is Hz. (iii) to show that the maximum kinetic energy of the hydrogen atom is J. (c) On the grid below, sketch a graph to show the variation with time t of the speed v of the hydrogen atom for one period of oscillation starting at t = 0. (There is no need to add values to the speed axis.) (3) 9/12

10 (d) Assuming that the motion of the hydrogen atom is simple harmonic, its frequency of oscillation f is given by the expression 1 f 2 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. Estimate, using your answer to (d)(i), the maximum acceleration of the hydrogen atom. (e) Methane is classified as a greenhouse gas. (i) Describe what is meant by a greenhouse gas. Electromagnetic radiation of frequency Hz is in the infrared region of the electromagnetic spectrum. Suggest, based on the information given in (b), why methane is classified as a greenhouse gas. 17. This question is about waves. (Total 17 marks) (a) With reference to the direction of energy transfer through a medium, distinguish between a transverse wave and a longitudinal wave (3) 10/12

11 (b) A wave is travelling along the surface of some shallow water in the x-direction. The graph shows the variation with time t of the displacement d of a particle of water. d / mm t / s Use the graph to determine for the wave (i) the frequency,.... the amplitude... (c) The speed of the wave in (b) is 15 cm s 1. Deduce that the wavelength of this wave is 2.0 cm (d) The graph in (b) shows the displacement of a particle at the position x = 0. On the axes below, draw a graph to show the variation with distance x along the water surface of the displacement d of the water surface at time t = s. 11/12

12 d / mm x/cm (3) (e) The wave encounters a shelf that divides the water into two separate depths. The water to the right of the shelf is deeper than that to the left of the shelf. direction of travel of wave wave fronts 30 shelf shallow water deep water The angle between the wavefronts in the shallow water and the shelf is 30. The speed of the wave in the shallow water is 15 cm s 1 and in the deeper water is 20 cm s 1. For the wave in the deeper water, determine the angle between the normal to the wavefronts and the shelf (3) (Total 14 marks) 12/12

13 Mark scheme 1. C 4. D 7. A 10. C 13. A 2. D 5. B 8. A 11. B 3. B 6. C 9. A 12. C 14. (a) longitudinal; 1 (b) (i) wavelength = 0.5 m; 1 amplitude = 0.5 mm; 1 (iii) correct substitution into speed = frequency wavelength; to give v = = 330 m s 1 ; 2 max [5] 15. Wave phenomena (a) (i) wave that transfers energy; 1 amplitude = 4.0mm; 1 wavelength = 2.4cm; 1 frequency = 1 ; 0.3 speed = ; = 3.3Hz; 1 = 8.0cms 1 ; 1 (b) (i) angle of incidence = 40 ; sin 40 sin r 1.4 r = 27 ; angle = 63 ; 3 Award [1 max] for angle of incidence = 50, r = 33. construction: wavefronts equally spaced; separation less in medium B; angle in medium B correct by eye; 3 [11] 13/12

14 Additional problems 16. Simple harmonic motion and the greenhouse effect (a) the force acting / accelerating (on the body) is directed towards equilibrium (position); and is proportional to its / the bodies displacement from equilibrium; 2 (b) (i) m; 1 T = s; f 1 ; = Hz 2 (iii) ω = (2 f) = (rad s 1 ); E max = mω x ; = J 2 (c) negative sine; starting at zero; with same frequency as displacement; (allow 2mm square) 3 (d) (i) k = (4 2 f 2 m p ) = ; 560 Nm 1 1 use of F = kx and F = ma; to give a ms ; (e) (i) infra red radiation radiated from Earth will be absorbed by greenhouse gases; and so increase the temperature of the atmosphere / Earth; 2 the natural frequency of oscillation (of a methane molecule) is equal to Hz; because of resonance the molecule will readily absorb radiation of this frequency; 2 [17] 14/12

15 17. (a) Transverse the particles (of the medium) vibrate at right angles; to the direction of energy transfer; Longitudinal the particles (of the medium) vibrate in the same direction as the direction of energy transfer; 3 (b) (i) time period = 0.13 s; 1 1 f = 7.7( 0.3) Hz; 2 T 0.13 Award full marks for bald correct answer. 8 mm; 1 v (c) = ; f 15 ; 7.7 = 1.95 cm 2.0 cm 2 (d) start at ( ) on y-axis; sine curve of amplitude 8 mm; wavelength 2 cm; 3 (e) sin 1 v1 use of sin 2 v2 v2 sin 2 sin 1; v 1 20 = sin30 to give 2 = 42 ; 15 angle = 48 ; 3 [14] 15/12

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