1. This question is about simple harmonic oscillations. A longitudinal wave travels through a medium from left to right. Graph 1 shows the variation with time t of the displacement x of a particle P in the medium. Graph 1 (a) For particle P, (i) state how graph 1 shows that its oscillations are not damped. (ii) calculate the magnitude of its maximum acceleration. IB Questionbank Physics 1
(iii) calculate its speed at t = 0.12 s. (iv) state its direction of motion at t = 0.12 s. (b) Graph 2 shows the variation with position d of the displacement x of particles in the medium at a particular instant of time. Graph 2 Determine for the longitudinal wave, using graph 1 and graph 2, (i) the frequency. IB Questionbank Physics 2
(ii) the speed. Graph 2 reproduced to assist with answering (c)(i). (c) The diagram shows the equilibrium positions of six particles in the medium. (i) On the diagram above, draw crosses to indicate the positions of these six particles at the instant of time when the displacement is given by graph 2. (3) IB Questionbank Physics 3
(ii) On the diagram above, label with the letter C a particle that is at the centre of a compression. (Total 14 marks) 2. This question is about simple harmonic motion (SHM), wave motion and polarization. (a) By reference to simple harmonic motion, state what is meant by amplitude....... (b) A liquid is contained in a U-tube. Diagram 1 Diagram 2 The pressure on the liquid in one side of the tube is increased so that the liquid is displaced as shown in diagram 2. When the pressure is suddenly released the liquid oscillates. The damping of the oscillations is small. (i) Describe what is meant by damping. IB Questionbank Physics 4
(ii) The displacement of the liquid surface from its equilibrium position is x. The acceleration a of the liquid in the tube is given by the expression a = 2g l x where g is the acceleration of free fall and l is the total length of the liquid column. Explain, with reference to the motion of the liquid, the significance of the minus sign. (iii) The total length of the liquid column in the tube is 0.32 m. Determine the period of oscillation. (3) IB Questionbank Physics 5
(c) A wave is travelling along a string. The string can be modelled as a single line of particles and each particle executes simple harmonic motion. The period of oscillation of the particles is 0.80 s. The graph shows the displacement y of part of the string at time t = 0. The distance along the string is d. (i) On the graph, draw an arrow to show the direction of motion of particle P at the point marked on the string. (ii) Determine the magnitude of the velocity of particle P. (4) IB Questionbank Physics 6
(iii) Show that the speed of the wave is 5.0 m s 1. (3) (iv) On the graph above, label with the letter X the position of particle P at t = 0.40 s. (d) The string in (c) is fixed at both ends and is made to vibrate in a vertical plane in its first harmonic. (i) Describe how the standing wave in the string gives rise to the first harmonic. (3) IB Questionbank Physics 7
(ii) Outline how a travelling wave in a string can be used to describe the nature of polarized light. (3) (e) James is wearing polarized sunglasses and views the sunlight reflected from the smooth surface of a lake. The angle θ is the angle between the surface of the lake and James s line of sight. Calculate the value of θ at which the reflected sunlight from the surface is minimized. The refractive index of the water is 1.3............. (Total 25 marks) IB Questionbank Physics 8
3. This question is about water wave motion. A small sphere, mounted at the end of a vertical rod, dips below the surface of shallow water in a tray. The sphere is driven vertically up and down by a motor attached to the rod. The oscillations of the sphere produce travelling waves on the surface of the water. (a) The diagram shows how the displacement of the water surface at a particular instant in time varies with distance from the sphere. The period of oscillation of the sphere is 0.027 s. Use the diagram to calculate, for the wave, (i) the amplitude. IB Questionbank Physics 9
(ii) the wavelength. (iii) the frequency. (iv) the speed. (b) The wave moves from region A into a region B of shallower water. The waves move more slowly in region B. The diagram (not to scale) shows some of the wavefronts in region A. IB Questionbank Physics 10
(i) With reference to a wave, distinguish between a ray and a wavefront. (ii) The angle between the wavefronts and the interface in region A is 60. The refractive index A n B is 1.4. Determine the angle between the wavefronts and the interface in region B. (iii) On the diagram above, construct three lines to show the position of three wavefronts in region B. IB Questionbank Physics 11
(c) Another sphere is dipped into the water. The spheres oscillate in phase. The diagram shows some lines in region A along which the disturbance of the water surface is a minimum. (i) Outline how the regions of minimum disturbance occur on the surface. (3) IB Questionbank Physics 12
(ii) The frequency of oscillation of the spheres is increased. State and explain how this will affect the positions of minimum disturbance. (Total 15 marks) 4. This question is about polarization. (a) State what is meant by polarized light....... IB Questionbank Physics 13
(b) Unpolarized light is incident on the surface of a plastic. The angle of incidence is θ. The reflected light is viewed through an analyser whose transmission axis is vertical. The variation with θ of the intensity I of the transmitted light is shown in the graph. (i) Explain why there is an angle of incidence, for which the intensity of the transmitted light is zero. IB Questionbank Physics 14
(ii) Calculate the refractive index of the plastic. (c) Unpolarized light from a source is split, so that there is a path difference of half a wavelength between the two beams. A lens brings the light to focus at point P on a screen. The lens does not introduce any additional path difference. State and explain whether any light would be observed at P, in the case in which the polarizers have their transmission axes (i) parallel. IB Questionbank Physics 15
(ii) at right angles to each other. (Total 9 marks) 5. This question is about standing waves. (a) State two properties of a standing (stationary) wave. 1....... 2....... (b) The diagram shows an organ pipe that is open at one end. The length of the pipe is l. The frequency of the fundamental (first harmonic) note emitted by the pipe is 16 Hz. (i) On the diagram, label with the letter P the position along the pipe where the amplitude of oscillation of the air molecules is the largest. IB Questionbank Physics 16
(ii) The speed of sound in the air in the pipe is 330 m s 1. Calculate the length l. (3) (c) Use your answer to (b)(ii) to suggest why it is better to use organ pipes that are closed at one end for producing low frequency notes rather than pipes that are open at both ends............. (Total 8 marks) 6. This question is about polarized light. (a) Distinguish between polarized and unpolarized light............. IB Questionbank Physics 17
(b) A beam of plane polarized light of intensity I 0 is incident on an analyser. The direction of the beam is at right angles to the plane of the analyser. The angle between the transmission axis of the analyser and the plane of polarization of the light is θ. In the position shown the transmission axis of the analyser is parallel to the plane of polarization of the light (θ = 0). On the axes, sketch a graph to show how the intensity I of the transmitted light varies with θ as the analyser is rotated through 180. (Total 4 marks) IB Questionbank Physics 18
7. This question is about microwave radiation. A microwave transmitter emits radiation of a single wavelength towards a metal plate along a line normal to the plate. The radiation is reflected back towards the transmitter. A microwave detector is moved along a line normal to the microwave transmitter and the metal plate. The detector records a sequence of equally spaced maxima and minima of intensity. (a) Explain how these maxima and minima are formed......................... (4) (b) The microwave detector is moved through 130 mm from one point of minimum intensity to another point of minimum intensity. On the way it passes through nine points of maximum intensity. Calculate the (i) wavelength of the microwaves. IB Questionbank Physics 19
(ii) frequency of the microwaves. (c) Describe and explain how it could be demonstrated that the microwaves are polarized................... (3) (Total 11 marks) IB Questionbank Physics 20
8. This question is about standing (stationary) waves. (a) Describe two ways that standing waves are different from travelling waves. 1....... 2....... (b) An experiment is carried out to measure the speed of sound in air, using the apparatus shown below. A tube that is open at both ends is placed vertically in a tank of water, until the top of the tube is just at the surface of the water. A tuning fork of frequency 440 Hz is sounded above the tube. The tube is slowly raised out of the water until the loudness of the sound reaches a maximum for the first time, due to the formation of a standing wave. (i) Explain the formation of a standing wave in the tube. IB Questionbank Physics 21
(ii) State the position in the tube that is always a node. (iii) The tube is raised a little further. Explain why the loudness of the sound is no longer at a maximum. (3) (c) The tube is raised until the loudness of the sound reaches a maximum for a second time. Between the two positions of maximum loudness, the tube has been raised by 36.8 cm. The frequency of the sound is 440 Hz. Estimate the speed of sound in air............. (Total 10 marks) IB Questionbank Physics 22
9. This question is about standing (stationary) waves. The diagram represents a standing wave of wavelength λ set up on a string of length L. The string is fixed at both ends. (a) For this standing wave (i) state the relationship between λ and L. (ii) label, on the diagram, two antinodes where the string is vibrating in phase. Label the antinodes with the letter A. (b) The standing wave has wavelength λ and frequency f. State and explain, with respect to a standing wave, what is represented by the product f λ................... (3) (Total 6 marks) IB Questionbank Physics 23
10. This question is about standing waves. A string that is fixed at both ends is made to vibrate in the fundamental (first harmonic) mode. The fixed ends of the string are at x = 0 and x =L. Each point on the string oscillates in simple harmonic motion. The displacement y of the string at a point x at time t is given by the equation πx where A = 12sin. 2 y = Acos(500πt) In these formulae x is in metres and t is in seconds. Using this equation, (a) explain why the amplitude of the standing wave is not constant....... (b) calculate the frequency of the standing wave.......... IB Questionbank Physics 24
(c) show that L = 2.0 m....... (Total 4 marks) 11. This question is about polarization. (a) A beam of unpolarized light of intensity I 0 is incident on a polarizer. The polarization axis of the polarizer is initially vertical as shown. The polarizer is then rotated by 180 in the direction shown. On the axes below, sketch a graph to show the variation with the rotation angle θ, of the transmitted light intensity I, as θ varies from 0 to 180. Label your sketch-graph with the letter U. IB Questionbank Physics 25
(b) The beam in (a) is now replaced with a polarized beam of light of the same intensity. The plane of polarization of the light is initially parallel to the polarization axis of the polarizer. The polarizer is then rotated by 180 in the direction shown. On the same axes in (a), sketch a graph to show the variation with the rotation angle θ, of the transmitted light intensity I, as θ varies from 0 to 180. Label your sketch-graph with the letter P. (Total 4 marks) 12. This question is about standing waves and organ pipes. (a) State one way in which a standing wave differs from a travelling wave....... IB Questionbank Physics 26
(b) An organ pipe of length L is closed at one end. On the diagrams, draw a representation of the displacement of the air in the pipe when the frequency of the note emitted by the pipe is the (i) fundamental (first harmonic) frequency f 1. (ii) second harmonic frequency f 2. (c) Use your answer to (b) to deduce an expression for the ratio f f 1 2................... (3) IB Questionbank Physics 27
(d) State, in terms of the boundary conditions of the standing waves that can be formed in the pipe, the reason why the ratio of the higher frequencies of the harmonics to that of the fundamental must always be an integer number....... (Total 7 marks) 13. This question is about standing waves. A string is attached between two rigid supports and is made to vibrate at its fundamental frequency (first harmonic) f. The diagram shows the displacement of the string at t = 0. (a) Draw the displacement of the string at time (i) t = 1 4 f (ii) t = 1 2 f IB Questionbank Physics 28
(b) The distance between the supports is 1.0 m. A wave in the string travels at a speed of 240 m s 1. Calculate the frequency of the vibration of the string............. (c) An organ pipe that is open at one end has the same fundamental frequency as the string in part (b). The speed of sound in air is 330 m s 1. Determine the length of the pipe............. (Total 6 marks) 14. This question is about polarization. (a) State what is meant by polarized light....... IB Questionbank Physics 29
(b) Polarized light of intensity I 0 is incident on an analyser. The transmission axis of the analyser makes an angle with the direction of the electric field of the light. (i) Calculate, in terms of I 0, the intensity of light transmitted through the analyser when = 60....... (ii) On the axes below, sketch a graph to show the variation with angle of the intensity of the transmitted light. (c) Outline how polarizing sunglasses reduce glare from a reflecting surface............. (3) (Total 7 marks) IB Questionbank Physics 30