A-LevelPhysicsSuperposition9702/52 · May/June 2020 · Q115 Marks

A student investigates stationary waves with an elastic cord of circular cross-section attached to a load, as shown in Fig. 1.1. [Figure 1.1] When the frequency of the vibrator is f, the cord vibrates with the stationary wave pattern shown. The student investigates how f varies with the cross-sectional area A of the cord. It is suggested that the relationship between f and A is f = 1 / (2L√(M/(kA))) where L is the distance between the two nodes, M is the mass of the load and k is a constant. Design a laboratory experiment to test the relationship between f and A. Explain how your results could be used to 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 • any safety precautions to be taken.

A student investigates stationary waves with an elastic cord of circular cross-section attached to a load, as shown in Fig. 1.1. [Figure 1.1] When the frequency of the vibrator is f, the cord vibrates with the stationary wave pattern shown. The student investigates how f varies with the cross-sectional area A of the cord. It is suggested that the relationship between f and A is f = 1 / (2L√(M/(kA))) where L is the distance between the two nodes, M is the mass of the load and k is a constant. Design a laboratory experiment to test the relationship between f and A. Explain how your results could be used to 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 • any safety precautions to be taken.[15]

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Mark scheme

Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.

[1] A is the independent variable and f is the dependent variable or vary A and measure f
[1] keep M constant
[1] labelled diagram of workable experiment including: elastic cord fixed at one end to a support • other end passed over a pulley • labelled pulley • labelled load
[1] vibrator connected to signal generator
[1] increase/decrease the frequency of the signal generator until stationary wave pattern is observed
[1] measure diameter of cord with micrometer/calipers
[1] plot a graph of f² against 1 / A or equivalent (e.g. Ig f against Ig A)
[1] relationship valid if a straight line passing through the origin is produced (for Ig f against Ig A, relationship valid if a straight line with gradient -1½)
[1] k = M / (gradient × 4 × L²) (for Ig f against Ig A, k = M / [10^(2 × y-intercept) × 4 × L²])
[D1] use safety goggles/safety screen to prevent injury to eyes from (moving) elastic cord/load or use cushion/sand box in case load falls
[D2] keep L constant
[D3] use cords of the same material/density
[D4] use CRO to determine f (or T)
[D5] method to determine T from CRO, e.g. period = time base × length of one wave
[D6] f = 1 / T
[D7] repeat measurement of diameter along cord and average
[D8] use of A = πd² / 4
[D9] measure mass of the load on top-pan balance
[D10] detail on determining frequency at the maximum amplitude, e.g. increase frequency until the amplitude starts to decrease, then decrease frequency

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