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A student investigates the sound from a horn attached to a car, as shown in Fig. 2.1.

Fig. 2.1 (not to scale)

A microphone is placed at the side of the road and connected to a frequency meter. The car travels towards the microphone. The frequency f of the sound detected by the microphone is read from the frequency meter.

The speed of the car is measured by two speed detectors. The two measurements of speed are $v_{1}$ and $v_{2}$ . The average speed v of the car is determined from $v_{1}$ and $v_{2}$ .

The experiment is repeated for different speeds of the car.
It is suggested that f and v are related by the equation

f=\frac{f_{\mathrm{s}} k}{k-v}

where $f_{\mathrm{s}}$ is the frequency of the sound emitted by the horn and k is a constant.

(a)

(c) (i) Plot a graph of $\frac{1}{f} / 10^{-3} \mathrm{~Hz}^{-1}$ against $v / \mathrm{m} \mathrm{s}^{-1}$ . Include error bars for v.

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(b)

(ii) Draw the straight line of best fit and a worst acceptable straight line on your graph. Label both lines.
(iii) Determine the gradient of the line of best fit. Include the absolute uncertainty in your answer.
gradient =

Figure for Question (b) — CAIE A-Level Physics A2

[ 2 ]

(c)

Determine the percentage uncertainty in k.

[ 1 ]

Percentage uncertainty in k with method shown.
$\text{percentage uncertainty}=\left(\frac{\Delta y\text{-intercept}}{y\text{-intercept}}+\frac{\Delta\text{ gradient}}{\text{gradient}}\right)\times100$
or correct substitution for max/min methods.

CAIE A-Level Physics A2 P5.4 Tables Graphs and Uncertainty Treatment Topic Practice

Question 1

Question (a)

Question (b)

Question (c)