Cambridge A Level Physics 9702 — 2015 May/June Paper 5 · Variant 2

1 A student is investigating how the intensity of the reflection of sound from a wall varies with the thickness of foam attached to the wall, as shown in Fig. 1.1. wall foam t Fig. 1.1 It is suggested that the intensity I of the reflected sound is related to the thickness t of the foam by the relationship I = I0e−αρt where I0 is the intensity of the sound before reflection, ρ is the density of the foam and α is a constant. Design a laboratory experiment to test the relationship between I and t. Explain how your results could be used to determine a value for α. You should draw a diagram, on page 3, showing the arrangement of your equipment. In your account you should pay particular attention to (a) the procedure to be followed, (b) the measurements to be taken, (c) the control of variables, (d) the analysis of the data, (e) the safety precautions to be taken. 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Mark scheme: 1 Planning (15 marks) Defining the problem (3 marks) P t is the independent variable and I (or amplitude of reflected signal) is the dependent variable, or vary t and measure I (or amplitude of reflected signal). [1] P Keep distance from the wall/foam to the speaker/microphone constant. [1] P Keep the amplitude or intensity I0 of the sound before reflection constant. [1] Methods of data collection (5 marks) M Labelled diagram of workable experiment including speaker, microphone/sound detector, foam and wall. [1] M Signal generator/a.c. power supply connected to speaker. [1] M Microphone connected to oscilloscope or sound (intensity) meter. [1] M Measure the thickness with a rule/micrometer/vernier calipers. [1] M Method to determine the density; ρ = m / V. [1] Method of analysis (2 marks) A Plot a graph of ln I against t. (Allow log I against t and lg I against t graphs.) [1] A α = – gradient / ρ (must be consistent with graph plotted) [1] Safety considerations (1 mark) S Precaution linked to loud sounds, e.g. use ear plugs/muffs/defenders. Allow switch off sound source to prevent damage to ears. [1] Additional detail (4 marks) D Relevant points might include [4] 1 Keep the frequency constant 2 Carry out experiment in a quiet room/no other sources of sound 3 Method to keep angles constant/positions of speaker and microphone constant. 4 Method and explanation to detect reflected sound from foam only, e.g. barrier, tube or method to avoid reflections 5 Method to determine mass, e.g. use scales/balance and method to determine volume 6 Relationship is valid if the graph is a straight line (ignore reference to y-intercept) 7 Method to check that emitted sound I0 is constant or method to check y-intercept is ln I0. 8 Intensity is proportional to the amplitude2. Do not allow vague computer methods.

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2 A student is investigating a circuit containing two horizontal parallel plates separated by an insulator. The circuit is set up as shown in Fig. 2.1. vibrating reed switch I A + plate power supply – area of l overlap w plate Fig. 2.1 An experiment is carried out to investigate how the current I varies with the area X of overlap of the parallel plates. The student measures the length l of overlap. To determine the area X of overlap, the student uses the relationship X = wl where w is the width of the plates. It is suggested that I and X are related by the equation I εE = fX d where E is the e.m.f. of the power supply, f is the frequency of the vibrating reed switch, d is the separation of the two parallel plates and ε is a constant. (a) A graph is plotted of I on the y-axis against X on the x-axis. Determine an expression for the gradient. gradient = ..................................................[1] (b) The width w of the plates has a value of 0.300 ± 0.005 m. Values of l and I are given in Fig. 2.2. l / m I / 10−6 A 0.160 ± 0.005 4.6 0.180 ± 0.005 5.3 0.210 ± 0.005 6.2 0.240 ± 0.005 7.1 0.270 ± 0.005 8.0 0.300 ± 0.005 8.8 Fig. 2.2 Calculate and record values of X / 10−2 m2 in Fig. 2.2. Include the uncertainties in X. [3] (c) (i) Plot a graph of I / 10−6 A against X / 10−2 m2. Include error bars for X. [2] (ii) Draw the straight line of best fit and a worst acceptable straight line on your graph. Both lines should be clearly labelled. [2] (iii) Determine the gradient of the line of best fit. Include the uncertainty in your answer. gradient = ..................................................[2] 9.5 9.0 I / 10–6 A 8.5 8.0 7.5 7.0 6.5 6.0 5.5 5.0 4.5 4.0 4 5 6 7 8 9 10 X / 10–2 m2

Mark scheme: 2 Analysis, conclusions and evaluation (15 marks) Expected Answer Additional Guidance ε Ef (a) A1 gradient = d (b) T1 X / 10–2 m2 T2 Allow a mixture of significant figures. 4.80 or 4.800 Must be table values. 5.40 or 5.400 6.30 or 6.300 7.20 or 7.200 8.10 or 8.100 9.00 or 9.000 U1 From ±0.2 to ±0.3 Allow more than one significant figure. (c) (i) G1 Six points plotted correctly Must be within half a small square. Do not allow “blobs”. Ecf allowed from table. U2 Error bars in X plotted All error bars to be plotted. Must be accurate to correctly less than half a small square. (ii) G2 Line of best fit Lower end of line must pass between (5.1, 5.0) and (5.3, 5.0) and upper end of line must pass between (8.5, 8.5) and (8.8, 8.5). G3 Worst acceptable straight line. Line should be clearly labelled or dashed. Steepest or shallowest Examiner judgement on worst acceptable line. possible line that passes Lines must cross. Mark scored only if error bars through all the error bars. are plotted. (iii) C1 Gradient of best fit line The triangle used should be at least half the length of the drawn line. Check the read-offs. Work to half a small square. Do not penalise POT. (Should be about 1 × 10–4.) U3 Uncertainty in gradient Method of determining absolute uncertainty: difference in worst gradient and gradient. (d) (i) C2 ε = 6.25 × 10–7 × gradient Do not penalise POT. (Should be about 6 or 7 × 10–11.) C3 F m–1 or C V–1 m–1 Allow A m–1 V–1 Hz–1 or A s m–1 V–1 or A2 s4 kg–1 m–3. Power of 10 must be correct. (ii) U4 Percentage uncertainty in ε 10.83% + percentage uncertainty in gradient (e) C4 f in the range 73.0 to 84.4 and Allow 73 to 84 for 2 s.f. given to 2 or 3 s.f. 5 . 0 × 10 −9 f = ε U5 Absolute uncertainty in f Clear working needed. Allow ecf from (d)(ii). Uncertainties in Question 2 (c) (iii) Gradient [U3] uncertainty = gradient of line of best fit – gradient of worst acceptable line uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient) (d) (ii) [U4] max gradient × max d max ε = min E × min f min gradient × min d min ε = max E × max f  ∆gradient ∆d ∆f ∆E  + + + × 100 % uncertainty =  d f E   gradient   ∆gradient 0.0002 10 0.2  =  + + +  × 100  gradient 0.0030 400 12.0  (e) [U5] max I × max d max f = min X × min ε × min E min I × min d min f = max X × max ε × max E  ∆I ∆d ∆l ∆E ∆ε   0.1 0.0002 0.001 0.2 ∆ε   ∆ε  ∆f =  + + 2 + +  f =  + + 2 + +  f =  0.107 +  f  I d l E ε   5.0 0.0030 0.500 12.0 ε   ε   10.7 + (d)(ii)    21.5 + % uncertainty in gradient   ∆f =  f =  f if (d)(ii) is correct  100    100  

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