CAIE A-Level Physics P5 Conclusions from Graphs

Practise using gradients and intercepts from plotted relationships to determine constants, link graph features to the model, and report values with units and uncertainty.

[Maximum number: 4]

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)

Determine the y-intercept of the line of best fit. Include the absolute uncertainty in your answer.

y \text {-intercept }=

[ 2 ]

(c)(iii)

Gradient determined with clear substitution of data points into $\Delta y / \Delta x$ .

Gradient must be negative.

Distance between data points must be greater than half the length of the drawn line.

Gradient determined of worst acceptable line with clear substitution of data points into $\Delta y / \Delta x$ .

uncertainty = (gradient of line of best fit - gradient of worst acceptable line)

or

uncertainty =1 / 2 (steepest worst line gradient - shallowest worst line gradient)

2(c)(iv)

y-intercept determined by substitution of correct point with consistent power of ten in m and y into y=m x+c.

y-intercept of worst acceptable line determined by substitution into y=m x+c.

uncertainty =y-intercept of line of best fit -y-intercept of worst acceptable line

or

uncertainty =1 / 2 (steepest worst line y-intercept - shallowest worst line y-intercept)

Marking guidance:

Do not accept ECF from false origin method.

(b)

Using your answers to (a), (c)(iii) and (c)(iv), determine the values of $f_{\mathrm{s}}$ and k. Include appropriate units.

\begin{gathered} f_{\mathrm{s}}= \\ k= \end{gathered}

[ 2 ]

$f_{\mathrm{s}}$ determined using y-intercept and $f_{\mathrm{s}}$ given to 2 , 3 or 4 significant figures and k given to 2 or 3 significant figures.
$f_{s}=\frac{1}{y \text {-intercept }}$

k determined using gradient with method shown and $f_{\mathrm{s}}$ and k given with SI units with appropriate powers of ten.
$\begin{aligned} k=-\frac{y \text {-intercept }}{\text { gradient }} \text { or } k=-\frac{1}{\text { gradient } \times f_{s}} \text { Units of } f_{\mathrm{s}}: \mathrm{Hz} \text { Units of } k: \mathrm{m} \mathrm{~s}^{-1} \end{aligned}$

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P5.5-Conclusions from constants, gradients and intercepts question 1

Question (a)

Question (b)