A student is investigating how the time for an electrical pulse to travel in a coaxial cable varies with the length of the cable. The pulse is reflected at one end of the cable. An oscilloscope is used to display the initial pulse and the reflected pulse. The trace on the oscilloscope is shown in Fig. 2.1. [Figure 2.1] The time t for the pulse to travel to the end of the cable and back is determined by measuring the distance d between the pulses on the screen, and then using the time-base and the relationship t = d × time-base. The initial length of the cable is L. A total length Z is removed from the cable and the experiment is repeated. It is suggested that t and Z are related by the equation v = 2(L-Z) / t where v is the speed of the pulse.

Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

1. [1] gradient = -2/v
2. [1] y-intercept = 2L/v
3. [1] First mark for all values of t correct.
4. [1] Second mark for uncertainties correct.
5. [1] Six points plotted correctly. Must be accurate to less than half a small square. No "blobs". Diameter of points must be less than half a small square.
6. [1] Error bars in t plotted correctly. All error bars to be plotted. Length of bar must be accurate to less than half a small square and symmetrical.
7. [1] Line of best fit drawn. If points are plotted correctly then upper end of line should pass between (4.8, 0.76) and (5.6, 0.76) and lower end of line should pass between (17.6, 0.64) and (18.8, 0.64). Line should not be from first to last plot.
8. [1] Worst acceptable line drawn (steepest or shallowest possible line). All error bars must be plotted.
9. [1] Gradient determined with a triangle that is at least half the length of the drawn line. Gradient must be negative.
10. [1] uncertainty = gradient of line of best fit – gradient of worst acceptable line
11. [1] uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient)
12. [1] y-intercept read-off y-axis to less than half small square or determined by substitution into y = mx + c.
13. [1] uncertainty = y-intercept of line of best fit – y-intercept of worst acceptable line
14. [1] uncertainty = ½ (steepest worst line y-intercept – shallowest worst line y-intercept)
15. [1] v determined from gradient and units for v and L correct with correct power of ten. v = -2 / gradient (c)(iii)
16. [1] L determined from y-intercept and v and L given to 2 or 3 significant figures. Correct substitution of numbers must be seen. L = (v/2) * y-intercept = (v/2) * (c)(iv) = (c)(iv) / (c)(iii)
17. [1] % uncertainty in v = % uncertainty in gradient
18. [1] % uncertainty in L = % uncertainty in y-intercept + % uncertainty in gradient
19. [1] % uncertainty in L = % uncertainty in y-intercept + % uncertainty in v
20. [1] Correct substitution of numbers must be seen.
21. [1] Maximum/minimum methods: Max L = max y-intercept × max v or max y-intercept / min gradient
22. [1] Min L = min y-intercept × min v or min y-intercept / max gradient