CAIE Physics (9702)

A student investigates stationary waves in a vertical tube using the apparatus shown in Fig. 2.1. from signal generator to oscilloscope loudspeaker tube bench stand The student slowly increases the frequency of the signal generator from zero and listens to the sound. The loudness of the sound varies several times between minimum and maximum as the frequency is increased. The lowest frequency giving maximum loudness is identified by n = 1. The next frequencies giving maximum loudness are identified by n = 2, 3, 4, 5 and 6. For each value of n, the student observes the trace on the oscilloscope screen. The student measures the distance d on the screen between two successive crests, as shown in Fig. 2.2. The student then determines the period T and frequency f of the signal. It is suggested that f and n are related by the equationf = (2n - 1)c where c is the speed of sound in air and h is the height of the tube. gradient =

The period T and frequency f are given by the equations Table 2.1 n d / cm / ms cm -1 T / ms f / Hz 1 1.4 ± 0.2 5 2 2.9 ± 0.2 1 3 3.6 ± 0.2 0.5 4 2.7 ± 0.2 0.5 5 2.1 ± 0.2 0.5 6 8.8 ± 0.2 0.1 Calculate and record values of T / ms and f / Hz in Table 2.1. Include the absolute uncertainties in T and f.

(i) Plot a graph of f / Hz against n. Include error bars for f.

Draw the straight line of best fit and a worst acceptable straight line on your graph. Label both lines.

Determine the gradient of the line of best fit. Include the absolute uncertainty in your answer. gradient = [2] f / Hz 1 2 3 4 5 6 7

The student measures the height of the tube. The student's values are: 83.5 cm 82.9 cm 83.3 cm 83.1 cm. Determine the average height h. Include the absolute uncertainty in h. h = cm

(i) Using your answers to (a), (c)(iii) and (d), determine the value of c. Include an appropriate unit. c =

Determine the percentage uncertainty in c. percentage uncertainty in c = %

The experiment is repeated with a different tube. When n = 2, the frequency is (130 ± 5) Hz. Determine the height h of this tube. Include the absolute uncertainty in your answer. h = m [2] [Total: 15] Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series.