JURONG JUNIOR COLLEGE Physics Department Tutorial: Wave Motion 1 The same progressive wave is represented by the following graphs. displacement y against time y p y displacement y against position x q 0 t 0 x Which of the following gives the speed of the wave? p q 1 A pq B C D q p pq [1] 2 The displacement-time graph (y - t) below represents the simple harmonic motion of a particle in a progressive wave travelling at a speed of 5.0 km s -1. y / m +2 0 10 20 30 40 t / s 2 Calculate its (a) frequency, (50 khz) [1] (b) amplitude (2 m) [1] (c) wavelength (100 mm) [1] Physics Dept Page 1 of 6
3 Parallel water waves of wavelength 10 m strike a straight sea wall. The wavefronts make an angle of 30 with the wall as shown below. Direction of Travel of wave wavefronts 30 sea wall What is the difference in phase at any instant between the waves at two points 5 m apart along the wall? (90 ) [3] 4 Transverse progressive sinusoidal waves of wavelength are passing vertically along a horizontal rope. P and Q are points on the rope 5 apart and the waves are traveling 4 from P to Q. Which of the following correctly describes Q at an instant when P is displaced upwards but is moving downwards? Displacement of Q Movement of Q A upwards downwards B upwards upwards C downwards upwards D downwards downwards E downwards stationary [1] 5 A ship s siren vibrates with displacement y, where y = a sin 200 t. This sound causes vibrations of the diaphragm of an eardrum of an observer 500 m away. The speed of sound is 335 m s -1. Calculate (a) the frequency of the sound, (100 Hz) [1] (b) the number of wavelength of this sound there are between the siren and the eardrum, in 5 sig.fig., (149.25) [2] (c) the phase difference between the motion of the siren and the eardrum, If the speed and distance data were reliable only to three significant figures, little confidence could be placed in your answer to (c). Explain this. (Ignore any possible phase differences between vibration surfaces and adjacent air) ( 2 rad) [3] Physics Dept Page 2 of 6
6 A point source of sound emits energy equally in all directions at a constant rate and a person 8 m from the source listens. After a while, the intensity of the source is halved. If the person wishes the sound to seem as loud as before, how far should he be now from the source? (4 2 m) [3] 7 A sound wave is emitted from a point source. The intensity of the sound wave is inversely proportional to the square of the distance from the source. At a distance r from the source, the amplitude of the wave is 8X. Determine the amplitude of the sound wave at a distance 2r from the source in terms of X. (4X) [2] 8 A 100 W light bulb is 10% efficient (that is, 90% of its output is invisible infra-red radiation and only 10% is visible light). A person can see the light with the naked eye from a distance of 20 km on a dark night. If the area of the pupil of the person s eye is 0.5 cm 2, find the power of the light that the eye of the person is receiving. (1.0 10-13 W) [3] 9 A progressive wave has amplitude 0.80 m and wavelength 4.0 m. At a given time the displacement is y = 0 m at x = 0 m, and y = 0.80 m at x = 1.0 m. (a) Sketch the displacement-position graph for 2 cycles of the wave. [1] (b) Calculate (i) the displacement at x = 0.5 m and 2.20 m; (0.57 m, 0.25 m) [2] (ii) the phase angles at x = 0.5 m and 1.60 m; (0.25 rad, 0.80 rad) [2] (iii) the phase difference between any two points which are 1.1 m apart on the wave. (0.55 rad) [1] (c) Explain the relationship of your answers in (b)(ii) and (b)(iii). [1] 10 Which of the following is true for all transverse waves? A They are all electromagnetic. B They can all be polarized. C They can all travel through a vacuum. D They all involve the oscillation of atoms. [1] Physics Dept Page 3 of 6
11 Figure below shows a beam of initially unpolarised light passing through three polariods P 1, P 2 and P 3. The polarizing axis of each Polaroid is shown by an arrow. Polaroids P 1 and P 2 are fixed, with their polarizing axes at 30 o to one another, and P 3 can be set with its polarizing axis at a variable angle θ to that of P 1. 30 o θ P 1 P 2 light beam P 3 For which values of do minimum intensity of the emergent light occur? A 30 o, 120 o, 210 o, 300 o B 90 o, 120 o, 270 o, 300 o C 60 o, 240 o D 90 o, 270 o E 120 o, 300 o [1] 12 (a) State the meaning of wavelength and frequency as applied to wave motion. [2] (b) Deduce, from definition of speed, the equation for the speed of a wave in terms of its wavelength and frequency. [1] (c) Distinguish between longitudinal and transverse waves. [2] (d) (e) State what is meant by the term polarization when applied to a wave. Explain why only transverse waves can be polarized but not longitudinal waves. [2] [H1/N11/II/6 (part)] Some films recently released have enabled viewing in three dimensions (3D). This can be done using two superimposed polarized images on the screen. One of the images is the scene as view by a left eye and the other the scene as viewed by a right eye. Explain how the images on the screen need to be polarized and how the spectacles of the cinema-goer also need to be polarized. [3] Physics Dept Page 4 of 6
Data Analysis Question 13 (a) [09SR/III/4] Sound waves travel at different speeds in different media. Fig. 14.1 shows the variation with time t of the distance d moved by a sound wave through air and water. d / km water air t / s Fig. 14.1 Use Fig. 14.1 to determine the speed of sound through air and water. (0.32 km s -1 ; 1.5 km s -1 ) [2] Physics Dept Page 5 of 6
(b) Three naval bases B 1, B 2 and B 3 are located along the circumference of a circle as shown in Fig. 14.2. B 1 B 2 B 3 A submarine in the vicinity sends out a signal which is detected at all 3 naval bases. The records of the variation with time of the signals detected at the naval bases are shown in Fig. 14.3 below. All 3 records were started at the same time. start of records Fig. 14.2 B 1 B 2 B 3 Fig. 14.3 time On each record, one pulse is made by sound waves travelling through air and the other, sound waves travelling through water. The time lag between the two pulses is referred to as the transmission lag. (i) Using evidence from the records in Fig. 14.3, state which naval base was closest to the submarine. [1] (ii) State two separate pieces of evidence to support your answer to (b)(i). [2] (iii) On the record produced by naval base B 2 in Fig. 14.3, circle the pulse caused by the sound wave travelling through water. Explain your answer. [2] (c) The transmission lags are 37 s, 33 s, and 26 s for naval bases B 1, B 2 and B 3 respectively. Use Fig. 14.1 to determine the distance of the submarine from each naval base. [15.0 km; 13.4 km; 10.6 km] [3] Physics Dept Page 6 of 6