Physics 9702/51 October/November 2021: question paper and mark scheme
Cambridge AS & A Level Physics (9702), Paper 5 Planning, Analysis and Evaluation, October/November 2021. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
A student investigates stationary sound waves in cylindrical tubes. Fig. 1.1 shows a stationary wave pattern in a tube which is open at both ends.
L
d
cylindrical tube
Fig. 1.1
The tube has length L and diameter d. The frequency of the sound for the stationary wave pattern shown is f.
There are a number of different tubes available.
It is suggested that the relationship between f and d is v
= 2L + kd f where v is the speed of sound in air and k is a constant.
Design a laboratory experiment to test the relationship between f and d.
Explain how your results could be used to determine values for k and v.
You should draw a diagram, on page 3, showing the arrangement of your equipment. In your account you should pay particular attention to:
● the procedure to be followed
● the measurements to be taken
● the control of variables
● the analysis of the data
● any safety precautions to be taken.
Diagram
…… [15]
Mark scheme
1 Defining the problem
diameter/d is the independent variable and frequency/f is the dependent variable or vary d and measure f 1
keep L constant or length (of tube) constant 1
Methods of data collection
labelled diagram of workable experiment including: 1
• tube supported
• (loud)speaker positioned in line with the tube
• (loud)speaker labelled
labelled microphone, positioned outside tube in line with tube, connected to labelled oscilloscope or correct circuit symbol 1
adjust/change frequency until maximum amplitude detected 1
use calipers to measure d 1
1 Method of analysis
1 1 1
plot a graph of against d or d against
f f
(Do not accept logarithmic graphs.)
1 1 1
for against d for d against
f f
v = gradient × k
or
2L or
v=
y -intercept gradient × 2L
v =−
y -intercept
1 1 1
for against d for d against
f f
k = gradient × v
or
or 2L
k =−
gradient × 2L y -intercept
k=
y -intercept
1 Additional detail including safety considerations 6
D1 wear ear defenders (to prevent damage to hearing/to avoid loud sounds)
or
use a low volume to prevent damage to hearing/to avoid loud sounds
D2 use a rule to measure L
D3 increase frequency from a low frequency to the first maximum amplitude
D4 method to determine f at maximum amplitude, e.g. increase frequency to f, then continue increasing frequency, and
then decrease frequency until value of f determined
D5 method to determine period from oscilloscope, e.g. no. of divisions × time-base
D6 for frequency/time period determined by oscilloscope, f = 1 / T
D7 repeat measurements of d and average in different directions/positions or along the tube
D8 perform experiment in a quiet room
D9 signal generator connected to (loud)speaker in diagram
D10 relationship valid if a straight line produced
(Do not accept through the origin.)
A student investigates the discharge of a capacitor in the circuit shown in Fig. 2.1.
E
C
V
R1 R2
P Q
Fig. 2.1
The student closes the switch and charges the capacitor.
The switch is opened and a stop-watch is started. The capacitor discharges through the two resistors of resistance R1 and R2 connected between P and Q. At a fixed time t the potential difference V across the capacitor is measured.
The experiment is repeated for different values of R1 and R2.
It is suggested that V, R1 and R2 are related by the equation
⎛V ⎞ t ln ⎝ ⎠ = –
E C(R1 + R2)
where E is the electromotive force (e.m.f.) of the battery and C is the capacitance of the capacitor.
1
(a) A graph is plotted of ln V on the y-axis against on the x-axis.
R1 + R2
Determine expressions for the gradient and y-intercept.
gradient = ……
y-intercept = ……
[1]
(b) Values of R1, R2, V and ln V are given in Table 2.1.
Each resistance value has a percentage uncertainty of ± 5%.
Table 2.1
1
R1 / kΩ R2 / kΩ (R1 + R2) / kΩ / 10−6 Ω−1 V/V ln (V / V)
R1 + R2
22 33 1.28 0.247
22 47 1.98 0.683
22 68 2.87 1.054
33 47 2.39 0.871
33 68 3.28 1.188
47 68 3.55 1.267
1
Calculate and record values of (R1 + R2) / kΩ and / 10−6 Ω−1 in Table 2.1.
R1 + R2
1
Include the absolute uncertainties in (R1 + R2) and . [2]
R1 + R2
1
(c) (i) Plot a graph of ln (V / V) against / 10−6 Ω−1.
R1 + R2
1
Include error bars for . [2]
R1 + R2
(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 absolute uncertainty in your answer.
gradient = …… [2]
1.3
1.2
1.1
In (V / V)
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
6 8 10 12 14 16 18 20
1
/ 10 –6 Ω–1
R1 + R2
(iv) Determine the y-intercept of the line of best fit. Include the absolute uncertainty in your answer.
y-intercept = …… [2]
(d) (i) Using your answers to (a), (c)(iii) and (c)(iv), determine the values of C and E. Include appropriate units.
Data: t = (60 ± 1) s
C = ……
E = ……
[2]
(ii) Determine the percentage uncertainty in C.
percentage uncertainty = …… % [1]
(e) The experiment is repeated using the same capacitor. Determine the value of (R1 + R2) that would give a value of V of 5.0 V at time t = 60 s.
(R1 + R2) = …… Ω [1]
[Total: 15]
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series.
Mark scheme
2(a) t 1
gradient = –
C
y-intercept = ln E
2(b) 1
(R1 + R2) / kΩ 1
/ 10–6 Ω
R1 + R2
55 (± 3) 18 or 18.2 ± 0.9
69 (± 3 or 4) 14 or 14.5 ± 0.7
90 (± 4 or 5) 11 or 11.1 ± 0.6
80 (± 4) 13 or 12.5 ± 0.6
101 (± 5) 9.9 or 9.90 or 9.901 ± 0.5
115 (± 6) 8.7 or 8.70 or 8.696 ± 0.4
1
Values of (R1 + R2) and correct as shown above.
R1 + R2
1 1
Absolute uncertainties in from ± 0.9 or ± 1 to ± 0.4 or ± 0.5.
R1 + R2
2(c)(i) Six points plotted correctly. 1
Must be accurate to half a small square. Diameter of points must be less than half a small square.
1 1
Error bars in plotted correctly.
R1 + R2
All error bars must be plotted. Total length of bar must be accurate to less than half a small square and symmetrical.
2(c)(ii) Line of best fit drawn. 1
Points must be balanced. Do not accept line from top point to bottom point.
Line must pass between (10.2, 1.10) and (10.8, 1.10) and between (16.7, 0.40) and (17.2, 0.40).
Worst acceptable line drawn (steepest or shallowest possible line that passes through all error bars). 1
All error bars must be plotted.
2(c)(iii) Negative gradient determined with clear substitution of data points into Δy / Δx. 1
Distance between data points must be at least half the length of the drawn line.
Gradient of worst acceptable line determined. 1
uncertainty = (gradient of line of best fit – gradient of worst acceptable line)
or
uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient)
2(c)(iv) y-intercept determined by substitution of point on line into y = mx + c. 1
y-intercept of worst acceptable line determined by substitution of point on line into y = mx + c. 1
uncertainty = y-intercept of line of best fit – y-intercept of worst acceptable line
or
uncertainty = ½ (steepest worst line y-intercept – shallowest worst line y-intercept)
Do not accept ECF from false origin method.
2(d)(i) C determined using gradient and C and E both given to two or three significant figures. 1
t 60
C=− =−
gradient (c)(iii)
E determined using y-intercept and C and E both given with correct SI unit. 1
E = e y -intercept
unit of C: F or C V–1 or s Ω–1
unit of E: V
2(d)(ii) Percentage uncertainty determined with method shown. 1
1 Δgradient
percentage uncertainty = + × 100
60 gradient
Clear substitution must be shown for maximum/minimum methods.
2(e) (R1 + R2) determined to at least two significant figures from (d)(i) or (c)(iii) and (c)(iv) with correct substitution including 1
signs and correct power of ten(s).
Do not accept ECF for POT from (c)(iii), (c)(iv) or (d).
t 1 60 1
( R1 + R2 ) = − ×
V
= − ×
C C lnV − ln E
ln
E
or
gradient (c)(iii)
( R1 + R2 ) = =
ln 5.0 − y -intercept 1.61 − (c)(iv)
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On this page, free: the mark scheme for AS & A Level Physics 9702/51, October/November 2021 (9702_w21_ms_51), and the question paper (9702_w21_qp_51), to read or download, with each question's marking points written out underneath.
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Physics 9702/51 for October/November 2021 is out of 30 marks, with 1 hour 15 minutes to answer it.
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