Planning, Analysis & Evaluation Instructions
Q. No.1 PLANNING QUESTION
2
1
Two students are having a discussion about an experiment in which the air inside a bell jar is
gradually removed. The sound of a ringing bell inside the jar is heard to decrease in intensity during
this process.
One student suggests that the frequency f of a sound wave and the pressure p are related by the
equation
f
kp2
where k is a constant.
Design a laboratory experiment to test the relationship between f and p and determine a value for
k. 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,
the safety precautions to be taken.
[15]
© UCLES 2014
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Diagram
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[Total: 15]
© UCLES 2014
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Question 1 Planning
Defining the problem
P
Vary pressure.
P
For different values of pressure, measure frequency.
D
Keep frequency of sound wave generated constant.
D
Keep temperature of the air constant.
Methods of data collection
M Labelled diagram of apparatus: container with source of sound.
M Method of varying p: e.g. use of pump to remove air/valve to allow air in.
M Method of measuring p: e.g. Bourdon gauge/pressure gauge/manometer.
M Use microphone connected to oscilloscope to measure frequency.
D
Method to determine the period of the wave including the use of the timebase.
D
f = 1/period.
Method of analysis
A
Plot f against p2; allow lg f against lg p.
A
Relationship is correct if graph is a straight line through the origin.
A
k = gradient.
Safety considerations and additional detail
D
Use a safety screen/goggles to prevent glass entering eyes if glass container shatters.
D
Use of y-axis on c.r.o. to check that initial sound has constant amplitude.
D
Need to seal points where wires pass through bell jar.
D
Use loud sound to obtain measurable readings at low pressures.
D
Check temperature with a thermometer.
Award P, M and A marks where seen. Award a maximum of 6 D marks.
© UCLES 2014
9702/05/SM/16
[Total: 15]
Q. 2) Analysis, conclusions and evaluation question:
Akhtar Mahmood (0333-4281759)
LGS, BLL, ALJT, ALBT, TCS-Ravi
TCS-ALCG, SALT Academy
teacher_786@hotmail.com
(a) Re-arrange the given equation as instructed to plot the graph and compare it to get an
expression of gradient and y-intercept (if any).
[1]
Examples:
Equation
R = cE
3/2
Instruction
Plot a graph of
2
R against E
E = IK
{June 19/51}
y = axn
y = aekx
{June 20/52}
3
A graph is
plotted of 1II on
the y-axis
x-axis
plot a graph of
log y against
log x
plot a graph of
ln y against x
A graph is
plotted of l
on the y-axis
against 1/T on
the x-axis
Working
Gradient
Y-Intercept
Akhtar Mahmood (0333-4281759)
LGS, BLL, ALJT, ALBT, TCS-Ravi
TCS-ALCG, SALT Academy
teacher_786@hotmail.com
(b)
Table of results:
Complete the table as instructed i.e.
[2]
Column Headings:
Provide column headings that include both the quantity and the units
(if any). In logarithmic quantities, units should be shown with the quantity
whose logarithm is being taken, e.g. ln (d / cm). The logarithm itself does not
have a unit.
Calculation of values:
Calculate the values as instructed and the no. of s.f in calculated
quantity should be equal to or one better than the least no. of s.f. of data used
in calculation. The number of significant figures may, if necessary, vary
down a column of values for a calculated quantity.
In logarithmic quantities, the number of decimal places should correspond to
the number of significant figures. For example, if L / cm is 76.5 (3 sf), then lg
(L / cm) should be either 1.884 (3 dp) or 1.8837 (4 dp).
Calculation of Uncertainties:
Absolute error can be calculated by methods read in AS level or use following relationships
i.e.
Absolute error = Max value
Best value
Absolute error = Best value
Min value
Absolute error = Max value Min value
2
Note: The no. of s.f. may be more than 1 s.f.
Example:
2
3
2
1. Calculate and record values of R and E in the table. Include the absolute errors in R .
Akhtar Mahmood (0333-4281759)
LGS, BLL, ALJT, ALBT, TCS-Ravi
TCS-ALCG, SALT Academy
teacher_786@hotmail.com
2. Calculate and record values of (1I/ )A-1. Include the absolute uncertainties in (1II)A-1
{june 19/51}
.
3. Calculate and record values of ln ( / 10-4 Pa s). Include the absolute uncertainties in ln ( / 10-4 Pa s).
{june 2020/52}
(c) Graph:
(i)
Plot the plots on the scaled graph provided:
Akhtar Mahmood (0333-4281759)
LGS, BLL, ALJT, ALBT, TCS-Ravi
TCS-ALCG, SALT Academy
teacher_786@hotmail.com [1]
Include error bars on the marked plots:
[1]
Error bar is the geometrical representation of uncertainty on the marked plots.
Error bars are either parallel to horizontal axis or vertical axis depending upon
the physical quantity taken along that axis and is marked by considering the
smallest graduation/box on the grid provided.
(ii)
Draw the straight line of best fit:
[1]
Draw the worst acceptable straight line:
[1]
The worst acceptable line should be either the steepest possible line or the shallowest
possible line that passes through the error bars of all the data points and is drawn
by joining the opposite ends of extreme end error bars.
Worst acceptable line should be distinguished from the line of best fit either by
being drawn as a broken line or by being clearly labelled.
(iii) Determination of Gradient & Y-intercept (if any):
Gradient:
Determine Gradient of best fit line
[2+2 or 1]
Determine Gradient of worst acceptable line
Gradient = (Gradient of best fit line in same no of d.p as in uncertainty) ± (Difference of
gradient of best and worst acceptable lines in 1 s.f)
Y-Intercept:
Use y = mx + c to get gradients of best and worst acceptable lines using respective
gradients and coordinates values.
Y-intercept = (Y-intercept of best fit line in same no of d.p as in uncertainty) ± (Difference
of y-intercepts of best and worst acceptable lines in 1 s.f)
Example:
Q. 1 {Specimen Paper June 2016}
Q.2 {june 19/51}
Q.3 {june 2020/52}
Akhtar Mahmood (0333-4281759)
LGS, BLL, ALJT, ALBT, TCS-Ravi
TCS-ALCG, SALT Academy
teacher_786@hotmail.com
(d) Use the expression of gradient & Y-intercept (if any) from part (a) and their
respective values from part (c)
[5 or 6]
to evaluate:
(i) Their values and uncertainties
(ii) Percentage errors
Example:
Q. {Specimen Paper June 2016}
5
2
In the early part of the twentieth century, experiments were carried out to measure the
range R and energy E of -particles in air using a number of different radioactive nuclides in the
thorium series.
It is suggested that R and E are related by the equation
3
R = cE 2
where c is a constant.
(a) A graph is plotted of R2 on the y-axis against E3 on the x-axis. Determine an expression for the
gradient in terms of c.
gradient
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(b) Values of R and E for a set of nuclides are given in Fig. 2.1.
R / 10 2 m
E / MeV
4.00
0.05
5.38
4.35
0.05
5.68
4.80
0.05
6.05
5.05
0.05
6.28
5.70
0.05
6.77
Fig. 2.1
Calculate and record values of R2 / 10 4 m2 and E3 / MeV3 in Fig. 2.1. Include the absolute
uncertainties in R2.
[3]
(c) (i)
Plot a graph of R2 / 10 4 m2 against E3 / MeV3. Include error bars for R2.
[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
© UCLES 2014
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36
34
32
R 2 / 10 –4 m2
30
28
26
24
22
20
18
16
14
150
175
200
225
250
3
275
E / MeV
© UCLES 2014
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300
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(d) Using your answer to (c)(iii), determine the value of c. Include the absolute uncertainty in your
value and an appropriate unit.
c
.......................................................... [3]
(e) The experiment is repeated for a different nuclide.
The range measured is 5.95 ± 0.05 cm.
(i)
(ii)
Using the relationship given and your answer to (d), determine the corresponding value
of E.
E
................................................. MeV [1]
percentage uncertainty
...................................................... % [1]
Determine the percentage uncertainty in E.
[Total: 15]
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Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local
Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
© UCLES 2014
9702/05/SP/16
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Question 2 Analysis, conclusions and evaluation
Mark
Expected Answer
Additional Guidance
(a)
A
Gradient = c2
(b)
T1
R 2/ 10 4 m2 and E3 / MeV3
T2
(c)(i)
(c)(ii)
(c)(iii)
(d)
16.0 or 16.00
18.9 or 18.92
23.0 or 23.04
25.5 or 25.50
32.5 or 32.49
0.4 to
[1]
Allow R 2 (10 4 m2) and E3 (MeV3)
156 or 155.7
183 or 183.3
221 or 221.4
248 or 247.7
310 or 310.3
0.6
Values must correspond to table.
U1
From
Allow more than one significant figure.
[3]
G1
Five points plotted correctly
Must be within half a small square. Penalise
‘blobs’. Ecf allowed from table.
U2
All error bars in R2 plotted
correctly
Must be accurate within half a small
square.
G2
Line of best fit
Allow ecf from points plotted incorrectly –
examiner judgement.
G3
Worst acceptable straight line.
Steepest or shallowest possible
line that passes through all the
error bars.
Line should be clearly labelled or dashed.
Should pass from top of top error bar to
bottom of bottom error bar or bottom of top
error bar to top of bottom error bar. Mark
scored only if all error bars are plotted.
[2]
C1
Gradient of best fit line
The triangle used should be at least half the
length of the drawn line. Check the readoffs. Work to half a small square. Do not
penalise POT. (Should be about 1.1 10 5)
U3
Uncertainty in gradient
Method of determining absolute uncertainty
Difference in worst gradient and gradient.
C2
c = gradient
C3
m MeV
U4
Absolute uncertainty in c
(e)(i)
C4
E given to 2 or 3 s.f.
(e)(ii)
U5
Percentage uncertainty in E
[2]
[2]
Gradient must be used. Should be about
0.0033.
Do not penalise POT.
32
Check working.
[3]
[1]
(
)
(
)
2 ∆R ∆c
1 ∆R ∆m
+
× 100 =
2
+
× 100
3 R
c
3
R
m
[1]
[Total: 15]
© UCLES 2014
9702/05/SM/16