CAIE A-Level Physics AS 8.1 Stationary Waves Questions

Practise explaining and investigating stationary waves with superposition, nodes, antinodes and resonance, then finding wavelength or phase from data.

Exam points

apply superposition to calculate or sketch resultant displacements and explain constructive/destructive combinations
explain and investigate stationary waves using opposite travelling waves, nodes, antinodes and experimental observations
determine wavelength and phase information from node/antinode positions or stationary-wave graphs

Covered syllabus points

8.1.1—And use the principle of superposition 8.1.2—Experiments that demonstrate stationary waves using microwaves, stretched 8.1.3—The formation of a stationary wave using a graphical method, and identify 8.1.4—Wavelength may be determined from the positions of nodes or antinodes of a

[Maximum number: 1]

Two waves superpose. A resultant wave pattern is formed.
Which statement about the two waves must be correct?

They have the same amplitude.

They are of the same type.

They are transverse waves.

They travel in opposite directions.

[Maximum number: 1]

A stationary sound wave is set up between a loudspeaker and a wall.
A microphone is connected to a cathode-ray oscilloscope (CRO) and is moved along a line directly between the loudspeaker and the wall. The amplitude of the trace on the CRO rises to a maximum at a position X , falls to a minimum and then rises once again to a maximum at a position Y.

The distance between X and Y is 33 cm . The speed of sound in air is $330 \mathrm{~m} \mathrm{~s}^{-1}$ .
Which diagram could represent the CRO trace of the sound received at X?

Figure for Question 2 — CAIE A-Level Physics AS — Option A

Figure for Question 2 — CAIE A-Level Physics AS — Option B

Figure for Question 2 — CAIE A-Level Physics AS — Option C

Figure for Question 2 — CAIE A-Level Physics AS — Option D

[Maximum number: 7]

(a)

A tube is open at both ends. A loudspeaker, emitting sound of a single frequency, is placed near one end of the tube, as shown in Fig. 3.1.

Fig. 3.1

The speed of the sound in the tube is $340 \mathrm{~ms}^{-1}$ . The length of the tube is 0.60 m .
A stationary wave is formed with an antinode A at each end of the tube and two antinodes inside the tube.

[ 7 ]

(i)

State what is meant by an antinode of the stationary wave.

[ 1 ]

(ii)

State the distance between a node and an adjacent antinode.

distance =m [1]

[ 1 ]

distance $=0.10 \mathrm{~m}$

(iii)

Determine, for the sound in the tube,
1. the wavelength,
wavelength = m
2. the frequency.
frequency = Hz

[ 3 ]

1. $\lambda=0.60 / 1.5$ $=0.40 \mathrm{~m}$
2. $v=f \lambda$ $\begin{aligned} f =340 / 0.40 =850 \mathrm{~Hz} \end{aligned}$

(iv)

Determine the minimum frequency of the sound from the loudspeaker that produces a stationary wave in the tube.
minimum frequency = Hz

[ 2 ]

$\lambda=2 \times 0.60$ or $\lambda=3 \times 0.40$ or f=850 / 3
f=280(283) Hz

[Maximum number: 1]

A tube is open at both ends. A loudspeaker, emitting sound of a single frequency, is placed near one end of the tube, as shown in Fig. 3.1.

Fig. 3.1

State what is meant by an antinode of the stationary wave.

[Maximum number: 1]

Two loudspeakers are connected to the same signal generator. The signal generator produces a single frequency. The loudspeakers face each other so that a stationary sound wave is set up in the region between the loudspeakers.

Figure for Question 5 — CAIE A-Level Physics AS

A microphone is connected to a cathode-ray oscilloscope (CRO) and positioned between the two loudspeakers.

The microphone is moved along a line joining the two loudspeakers.
The signal on the CRO shows 5 maximum amplitudes as the microphone moves. The microphone moves a distance of 2.0 m from the position that gives the first maximum to the position that gives the fifth maximum.

What is the wavelength of the sound wave?

0.40 m

0.50 m

0.80 m

$1.0 \mathrm{~m}$

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Covered syllabus points

Question 1

Question 2

Question 3

Question (a)

Question (i)

Question (ii)

Question (iii)

Question (iv)

Question 4

Question 5