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Date May 2017 Marks available 2 Reference code 17M.3.SL.TZ2.1
Level Standard level Paper Paper 3 Time zone Time zone 2
Command term State Question number 1 Adapted from N/A

Question

A radio wave of wavelength \(\lambda \) is incident on a conductor. The graph shows the variation with wavelength \(\lambda \) of the maximum distance d travelled inside the conductor.

For \(\lambda \) = 5.0 x 105 m, calculate the

The graph shows the variation with wavelength \(\lambda \) of d 2. Error bars are not shown and the line of best-fit has been drawn.

A student states that the equation of the line of best-fit is d 2 = a + b\(\lambda \). When d 2 and \(\lambda \) are expressed in terms of fundamental SI units, the student finds that a = 0.040 x 10–4 and b = 1.8 x 10–11.

Suggest why it is unlikely that the relation between d and \(\lambda \) is linear.

[1]
a.

fractional uncertainty in d.

[2]
b.i.

percentage uncertainty in d 2.

[1]
b.ii.

State the fundamental SI unit of the constant a and of the constant b.

[2]
c.i.

Determine the distance travelled inside the conductor by very high frequency electromagnetic waves.

[2]
c.ii.

Markscheme

it is not possible to draw a straight line through all the error bars
OR
the line of best-fit is curved/not a straight line

 

Treat as neutral any reference to the origin.

Allow “linear” for “straight line”.

[1 mark]

a.

d = 0.35 ± 0.01 AND Δd = 0.05 ± 0.01 «cm»

«\(\frac{{\Delta d}}{d} = \frac{{0.5}}{{0.35}}\)» = 0.14

OR

\(\frac{1}{7}\) or 14% or 0.1

 

Allow final answers in the range of 0.11 to 0.18.

Allow [1 max] for 0.03 to 0.04 if \(\lambda \) = 5 × 106 m is used.

[2 marks]

b.i.

28 to 30%

 

Allow ECF from (b)(i), but only accept answer as a %

[1 mark]

b.ii.

a: m2

b: m

 

Allow answers in words

[2 marks]

c.i.

ALTERNATIVE 1 – if graph on page 4 is used

d 2 = 0.040 x 10–4 «m2»

d = 0.20 x 10–2 «m»

ALTERNATIVE 2 – if graph on page 2 is used

any evidence that d intercept has been determined

d = 0.20 ± 0.05 «cm»

 

 

For MP1 accept answers in range of 0.020 to 0.060 «cm2» if they fail to use given value of “a”.

For MP2 accept answers in range 0.14 to 0.25 «cm» .

[2 marks]

c.ii.

Examiners report

[N/A]
a.
[N/A]
b.i.
[N/A]
b.ii.
[N/A]
c.i.
[N/A]
c.ii.

Syllabus sections

Core » Topic 1: Measurements and uncertainties » 1.1 – Measurements in physics
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