Question 4
4
9 marks
Question 4(a)
4(a)
State two features of a stationary wave that distinguish it from a progressive wave. 1. 2.
Mediumstructured2 marks
Answer
e.g. no energy transfer amplitude varies along its length/nodes and antinodes neighbouring points (in inter-nodal loop) vibrate in phase, etc. (any two, 1 mark each to max 2 B2
Question 4(b)
4(b)
A long tube is open at one end. It is closed at the other end by means of a piston that can be moved along the tube, as shown in Fig. 4.1. A loudspeaker producing sound of frequency 550 Hz is held near the open end of the tube. The piston is moved along the tube and a loud sound is heard when the distance L between the piston and the open end of the tube is 45 cm . The speed of sound in the tube is \(330 \mathrm{~ms}^{-1}\).
structured4 marks
Question 4(b)(i)
4(b)(i)
Show that the wavelength of the sound in the tube is 60 cm .
Mediumstructured1 marks
Answer
\(\lambda=60 \mathrm{~cm}\).......................................................................... . A0
Question 4(b)(ii)
4(b)(ii)
On Fig. 4.1, mark all the positions along the tube of 1. the displacement nodes (label these with the letter N ), 2. the displacement antinodes (label these with the letter A).
Mediumstructured3 marks
Answer
antinode labelled at open end of tube B1 additional node and antinode in correct positions along tube .............. B1
Question 4(c)
4(c)
The frequency of the sound produced by the loudspeaker in (b) is gradually reduced. Determine the lowest frequency at which a loud sound will be produced in the tube of Use length \(L=45 \mathrm{~cm}\). frequency = Hz
Hardstructured3 marks
Answer
at lowest frequency, length \(=\lambda / 4 \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . . \quad\) C1 \(\lambda=1.8 \mathrm{~m}\) = 180 Hz A1
Question 5
5
A stretched string PQ has length 1.2 m . One end of the string is attached to a vibration generator and the other end is attached to a wall, as shown in Fig. 5.1. The vibration generator is switched on and a stationary wave is formed on the string. The string is shown at one instant of time in Fig. 5.2.
structured8 marks
Question 5(a)
5(a)
Explain how a stationary wave is formed between the vibration generator and the wall.
Mediumstructured2 marks
Answer
wave(s) (travel along string and) reflect at fixed point / wall / Q / end / vibration generator / P B1 incident and reflected waves superpose B1
Question 5(b)
5(b)
Calculate the wavelength of the stationary wave shown in Fig. 5.2. wavelength = m
Easystructured1 marks
Answer
0.80 m A1
Question 5(c)
5(c)
Fig. 5.3 shows the stationary wave at time t=0 when all points on the wave are at their maximum displacements. The period of the wave is 0.16 s . On Fig. 5.3 , sketch the shape of the stationary wave at time \(t=0.24 \mathrm{~s}\).
Mediumstructured2 marks
Answer
same wavelength as original throughout and passing through intersection of solid and dashed lines B1 reflected in dashed line and of same amplitude B1
Question 23
23
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?
Mediummcq1 marks
Answer
B
Question 23
23
A stationary wave is produced by two loudspeakers emitting sound of the same frequency. When a microphone is moved between X and Y , a distance of 1.5 m , six nodes and seven antinodes are detected. What is the wavelength of the sound? 0.50 m 0.43 m 0.25 m \(0.21 \mathrm{~m}\)
Mediummcq1 marks
Answer
A
Question 5
5
Fig. 5.1 shows a string stretched between two fixed points P and Q. A vibrator is attached near end P of the string. End Q is fixed to a wall. The vibrator has a frequency of 50 Hz and causes a transverse wave to travel along the string at a speed of \(40 \mathrm{~ms}^{-1}\).
structured8 marks
Question 5(a)
5(a)
2 marks
Question 5(a)(ii)
5(a)(ii)
Explain how this arrangement may produce a stationary wave on the string.
Mediumstructured2 marks
Answer
waves (travel along string and) reflect at Q / wall / fixed end B1 incident and reflected waves interfere / superpose B1 [2]
Question 5(b)
5(b)
The stationary wave produced on PQ at one instant of time t is shown on Fig. 5.2. Each point on the string is at its maximum displacement.
structured6 marks
Question 5(b)(i)
5(b)(i)
On Fig. 5.2, label all the nodes with the letter N and all the antinodes with the letter A.
Easystructured2 marks
Answer
nodes labelled at P, Q and the two points at zero displacement B1 antinodes labelled at the three points of maximum displacement B1 [2]
Question 5(b)(ii)
5(b)(ii)
Use your answer in (a)(i) to calculate the length of string PQ . length = m
Mediumstructured1 marks
Answer
\((1.5 \lambda\) for PQ hence \(\mathrm{PQ}=0.8 \times 1.5)=1.2 \mathrm{~m} \quad \mathrm{~A} 1\)
Question 5(b)(iii)
5(b)(iii)
On Fig. 5.2, draw the stationary wave at time \((t+5.0 \mathrm{~ms})\). Explain your answer.
Hardstructured3 marks
Answer
\(T=1 / f=1 / 50=20 \mathrm{~ms}\) C1 5 ms is \(\frac{1}{4}\) of cycle A1 horizontal line through PQ drawn on Fig. 5.2 B1 [3]