A-LevelPhysicsSuperposition9702/23 · May/June 2019 · Q59 Marks

A vertical tube of length 0.60 m is open at both ends, as shown in Fig. 5.1. [Figure 5.1] An incident sinusoidal sound wave of a single frequency travels up the tube. A stationary wave is then formed in the air column in the tube with antinodes A at both ends and a node N at the midpoint.

(a)Explain how the stationary wave is formed from the incident sound wave. ......................................................................................................................................................................................................................................................................................................................................................................................................................................................... [2][2]
(b)On Fig. 5.2, sketch a graph to show the variation of the amplitude of the stationary wave with height h above the bottom of the tube. [Figure 5.2] [2][2]
(c)(i)For the stationary wave, state: the direction of the oscillations of an air particle at a height of 0.15 m above the bottom of the tube ......................................................................................................................................... [1][1]
(c)(ii)the phase difference between the oscillations of a particle at a height of 0.10 m and a particle at a height of 0.20 m above the bottom of the tube. phase difference = .................................................................... ° [1][1]
(d)The speed of the sound wave is 340 m s⁻¹. Calculate the frequency of the sound wave. frequency = .......................................................................... Hz [2][2]
(e)The frequency of the sound wave is gradually increased. Determine the frequency of the wave when a stationary wave is next formed. frequency = .......................................................................... Hz [1][1]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.

Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

[B1] (incident) wave reflects at end/top of tube
[B1] (incident) wave and reflected wave interfere/superpose
[B1] line has maximum value of amplitude at h = 0 and h = 0.60 m only
[B1] line has minimum/zero value of amplitude at h = 0.30 m only
[B1] vertical/along length of tube/along axis of tube
[A1] phase difference = 0
[C1] v = fλ
[A1] = 340 / (2 × 0.60)
[A1] f = 340/0.60