1. Data analysis question.

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These rings were produced as a result of interference of monochromatic light.

1 1. Data analysis question. The photograph below shows a magnified image of a dark central disc surrounded by concentric dark rings. These rings were produced as a result of interference of monochromatic light. The graph below shows how the ring diameter D varies with the ring number n. The innermost ring corresponds to n = 1. The corresponding diameter is labelled in the photograph. Error bars for the diameter D are shown. IB Questionbank Physics 1

2 (a) State one piece of evidence that shows that D is not proportional to n (b) On the graph opposite, draw the line of best fit for the data points. (2) (c) It is suggested that the relationship between D and n is of the form D = cn p where c and p are constants. Explain what graph you would plot in order to determine the value of p (3) IB Questionbank Physics 2

3 1 (d) Theory suggests that p = and so D 2 = kn (where k = c 2 ). 2 A graph of D 2 against n is shown below. Error bars are shown for the first and last data points only. (i) Using the first graph, calculate the percentage uncertainty in D 2, of the ring n = 7. (2) (ii) Based on the second graph, state one piece of evidence that supports the relationship D 2 = kn. IB Questionbank Physics 3

4 (iii) Use the second graph to determine the value of the constant k, as well as its uncertainty. (4) (iv) State the unit for the constant k. (Total 14 marks) IB Questionbank Physics 4

5 2. Data analysis question. The speed v of waves on the surface of deep water depends only on the wavelength λ of the waves. The data gathered from a particular region of the Atlantic Ocean are plotted below. The uncertainty in the speed v is ±0.30 m s 1 and the uncertainty in λ is too small to be shown on the diagram. (a) Draw a best fit line for the data. (b) State, with reference to the line you have drawn in (a), (i) why v is not directly proportional to λ. IB Questionbank Physics 5

6 (ii) the value of v for λ = 39 m. (c) It is suggested that the relationship between v and λ is of the form v = a λ where a is a constant. To test the validity of this hypothesis, values of v 2 against λ are plotted below. (i) Use your answer to (b)(ii) to show that the absolute uncertainty in v 2 for a wavelength of 39 m is ±5 m 2 s 2. (3) IB Questionbank Physics 6

7 (ii) The absolute uncertainty in v 2 for a wavelength of 2.5 m is ±1 m 2 s 2. Using this value and the value in (c)(i), construct error bars for v 2 at the data points for λ = 2.5 m and 39 m. (iii) State why the plotted data in (c)(ii) suggest that it is likely that v is proportional to λ. (iv) Use the graph above to determine the constant a. (3) (v) Theory shows that a = k. Determine a value for k. 2 π (Total 12 marks) IB Questionbank Physics 7

8 3. 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. (2) IB Questionbank Physics 8

9 (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 = 2 g 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. (2) (iii) The total length of the liquid column in the tube is 0.32 m. Determine the period of oscillation. (3) IB Questionbank Physics 9

(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.

10 (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 10

11 (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 11

12 (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 (2) (Total 25 marks) IB Questionbank Physics 12

13 4. This question is about standing (stationary) waves. (a) Describe two ways that standing waves are different from travelling waves (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. (2) IB Questionbank Physics 13

14 (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 (2) (Total 10 marks) IB Questionbank Physics 14

15 5. This question is about the Doppler effect. The sound emitted by a car s horn has frequency f, as measured by the driver. An observer moves towards the stationary car at constant speed and measures the frequency of the sound to be f. (a) Explain, using a diagram, any difference between f and f (3) (b) The frequency f is Hz. An observer moves towards the stationary car at a constant speed of 15.0 m s 1. Calculate the observed frequency f of the sound. The speed of sound in air is m s (2) (Total 5 marks) IB Questionbank Physics 15

16 6. 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. (2) (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 16

17 7. This question is about the eye and resolution. A student measures the aperture of the iris of one of her eyes as 2.0 mm in sunlight and 7.0 mm in moonlight. The intensity at her eye of sunlight is 106 times greater than the intensity of moonlight. (a) (i) Determine the following ratio. power of light entering the eye in sunlight power of light entering the eye in moonlight (3) (ii) Suggest why your answer in (a)(i) indicates that the change in diameter of the iris is not the principal mechanism by which the eye is able to adjust to different light intensities. (b) (i) State the Rayleigh criterion. (2) IB Questionbank Physics 17

18 (ii) Suggest, with reference to the Rayleigh criterion, whether the ability of the eye to resolve the image of two objects is greater in sunlight or in moonlight. (4) (c) Outline the different functions of the rods and the cones on the retina of the eye in their response to sunlight and to moonlight. Rods: Cones: (4) (Total 14 marks) 8. (a) line of best fit is not straight / line of best fit does not go through origin; 1 (b) smooth curve; that does not go outside the error bars; 2 Ignore extrapolations below n = 1. IB Questionbank Physics 18

19 (c) we can re write the suggested relation as log D = log c + p log n; now we can plot a graph of log D versus log n; the slope of the (straight line) graph is equal to p; 3 Accept logs in any base. (d) (i) absolute uncertainty in diameter D is ±0.08cm; giving a relative uncertainty in D of 2 = 0.13 or 13%; Award [2] if uncertainty is calculated for a different ring number. (ii) it is possible to draw a straight line that passes through the origin (and lies within the error bars); or the ratio of D 2 is constant for all data points; 1 n (iii) gradient = k; calculation of gradient to give 0.23 (accept answers in range 0.21 to 0.25); evidence for drawing or working with lines of maximum and minimum slope; answers in the form k = 0.23± 0.03; 4 Accept an uncertainty in k in range 0.02 to First marking point does not need to be explicit. (iv) cm 2 ; 1 [14] 9. (a) smooth curve through all the error bars; 1 (b) (i) the graph is not linear/a straight line (going through the error bars) / does not go through origin; 1 (ii) 7.7 m s 1 ; 1 1 Accurate reading from their graph to within square. 2 Allow ECF from (a). IB Questionbank Physics 19

20 (c) (i) 0. 3 % uncertainty in v = = = 3.9%; 0. 7 doubles 3.9% (allow ECF from (b)(ii)) to obtain % uncertainty in v 2 (= 7.8%); absolute uncertainty (= ±[ ]) = 4.6; (= ±5 m 2 s 2 ) 3 or calculates overall range of possible value as ; (allow ECF) squares values to yield range for v 2 of 54.8 to 64; (allow ECF) so error range becomes 9.2 hence ±4.6; (must see this value to 2 sig fig or better to award this mark) 1 (ii) correct error bars added to first point (± square) and 2 last but one point (±2.5 squares); (judge by eye) 1 (iii) a straight line/linear graph can be drawn that goes through origin; 1 (iv) uses triangle to evaluate gradient; (triangle need not be shown if read offs clear, read offs used must lie on candidate s drawn line) to arrive at gradient value of 1.5 ± 0.2; (unit not required) recognizes that gradient of graph is a 2 and evaluates a = 1.2 ± 0.2 ( m 2 s or 1 1 ); 3 candidate line drawn through origin and one data point read; correct substitution into v 2 = a 2 λ; (a 2 does not need to be evaluated for full credit) a = 1.2 ± 0.2( m s ); 1 Award [2 max] if line does not go through origin allow square. 2 Award [1 max] if one or two data points used and no line drawn. (v) k = 9.4 m s 2 ; (allow ECF from (c)(iv)) 1 [12] 10. (a) the maximum displacement of the system from equilibrium/ from centre of motion / OWTTE; 1 IB Questionbank Physics 20

21 (b) (i) the amplitude of the oscillations/(total) energy decreases (with time); because a force always opposes direction of motion/there is a resistive force/there is a friction force; 2 Do not allow bald friction. (ii) the displacement and acceleration/force acting on (the surface) are in opposite directions; 2 (iii) ω = 2 g l ; T = 2 π ; = 0.80 s; 3 (c) (i) upwards; 1 (ii) y 0 = 0.050(m) and y = 0.030(m); 2 π ω = = 7.85 (rad s 1 ); v = [ ] [ ] ; = 0.31 m s 1 ; (allow working in cm to give 31cm s 1 ) 4 (iii) λ = 4.0 m; 1 recognition that f = (= 1.25); (f λ =)v = ; (= 5.0 m s 1 ) 3 (iv) y = 3.0 cm, d = 0.6m ; 1 (d) (i) wave reflects at ends (of string); interference/superposition occurs (between waves); regions of maximum displacement/zero displacement form (that do not move)(*); one region of max displacement/antinode forms at centre with zero displacement/node at each end(*); (* allow these marking points from a clear diagram ) 3 max IB Questionbank Physics 21

22 (ii) the waves (in a string) are transverse and vibrate only in one plane; light waves are transverse electromagnetic waves; (and) for polarized light the electric field vector vibrates only in one plane; 3 (e) Brewster angle = tan 1 [1.3] = 52 ; θ = (90 52 =) 38 ; 2 [25] 11. (a) energy is propagated by travelling waves / energy is not propagated by standing waves; amplitude constant for travelling waves / amplitude varies with position for standing waves; phase varies with position for travelling waves / phase constant for standing waves; travelling waves do not have nodes and antinodes / standing waves do have nodes and antinodes; travelling waves can have any wavelength/frequency / standing waves can only have certain wavelengths/frequencies (to fit boundary conditions); 2 max (b) (i) wave from tuning fork travels down tube and is reflected; incident and reflected waves interfere/superpose/combine/ add together to give a standing wave (that fits the boundary conditions); 2 (ii) the surface of the water (in/at the bottom of the tube); 1 (iii) the length of the air column has changed; boundary conditions can no longer be met / the length is no longer equal to one quarter of a wavelength; hence a standing wave cannot form / resonance no longer occurs / natural frequency of air column no longer equal to frequency of sound; 3 (c) λ = λ = m; 2 v = f λ = = 320 m s 1 ; 2 [10] IB Questionbank Physics 22

23 12. (a) circular wavefronts around source, equally spaced; moving observer intercepts more wavefronts per unit time / the time between intercepting successive wavefronts is less; hence observes a higher frequency / f > f; or circular wavefronts around source, equally spaced; the velocity of the sound waves with respect to the observer is greater; v since f =, observed frequency is also greater; 3 λ v + u (b) f = f = 300 ; v 330 = 314 Hz; Award [0] for use of moving source formula. Award [1] for use of v u o to give 286 Hz. 2 [5] L 13. (a) (i) L = 4λ or λ = ; 1 4 (ii) two antinodes labelled; with separation of integral number of wavelengths; 2 (b) f λ is the speed of the wave; standing wave formed by interference of an incident and a reflected progressive wave; speed is the speed of this progressive wave; 3 [6] 14. (a) (i) power = area intensity; ratio = 10 6 ; 7. 0 = ; 3 (ii) if iris were to be the principal mechanism, then ratio would 7 need to be about or ; 1 7 IB Questionbank Physics 23

24 (b) (i) for two images (of two objects) just to be distinguished/ to be seen as separate images; maximum of one diffraction pattern must lie on first minimum of second; 2 (ii) ( ) λ images resolved when θ ; b where θ is angle subtended at eye by object and b is the diameter of the pupil; wavelength unchanged; larger diameter, better resolution; (accept vice versa) 4 (c) rods: scotopic vision / black and white vision; function best in low light intensity such as moonlight; cones: photopic vision / colour vision; function best in high light intensity such as sunlight; 4 Award [3 max] for omission of reference to moonlight and sunlight. [14] IB Questionbank Physics 24

A longitudinal wave travels through a medium from left to right.

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