CAIE A-Level Physics 8 Superposition

Practise applying superposition to waves, analysing stationary waves, diffraction and coherent interference, calculating related quantities and interpreting practical experiments.

Exam points

apply superposition to progressive and stationary-wave patterns, including resultant displacement, nodes, antinodes and wavelength
interpret and compare diffraction and interference patterns using aperture, wavelength, coherence, phase and path difference
calculate double-slit and diffraction-grating quantities from their governing relationships
describe wave experiments that demonstrate stationary waves, diffraction, interference or wavelength measurement

Covered syllabus points

8.1 Stationary waves 8.2 Diffraction 8.3 Interference 8.4 The diffraction grating

[Maximum number: 5]

(a)

A microwave of intensity $I_{0}$ and amplitude $A_{0}$ meets another microwave of the same frequency and of intensity $\frac{1}{4} I_{0}$ travelling in the opposite direction. Both microwaves are vertically plane polarised and superpose where they meet.

[ 5 ]

(i)

Explain, without calculation, why these two waves cannot form a stationary wave with zero amplitude at its nodes.

[ 2 ]

(ii)

Determine, in terms of $A_{0}$ , the maximum amplitude of the wave formed.
maximum amplitude = $A_{0}[3]$

[ 3 ]

$I \propto A^{2}$

C1

$A^{2} / A_{0}{ }^{2}=\left(I_{0} / 4\right) / I_{0}$ $A=0.5 A_{0}$

C1

Marking guidance:

maximum amplitude $=A_{0}+0.5 A_{0}$ $=1.5 A_{0}$

A1

[Maximum number: 8]

(a)

A diffraction grating is used to determine the wavelength of light.

[ 5 ]

(i)

Describe the diffraction of light at a diffraction grating.

[ 2 ]

(ii)

By reference to interference, explain

[ 3 ]

1. waves (from each element/slit) overlap/meet/superpose

with a phase difference/path difference of zero

2. phase difference is $360^{\circ}$ / path difference of $\lambda$

(i)

1. the zero order maximum,

(ii)

2. the first order maximum.

[ 3 ]

(b)

A diffraction grating is used with different wavelengths of light. The angle $\theta$ of the second order maximum is measured for each wavelength. The variation with wavelength $\lambda$ of $\sin \theta$ is shown in Fig. 5.1.

Fig. 5.1

[ 3 ]

(i)

Use the gradient determined in (i) to calculate the slit separation d of the diffraction grating.

[ 2 ]

$d \sin \theta=n \lambda$

d=n / gradient

C1

$=2 / 8.0 \times 10^{5}=2.5 \times 10^{-6} \mathrm{~m}$

A1

(ii)

On Fig. 5.1, sketch a line to show the results that would be obtained for the first order maxima.

[ 1 ]

straight line drawn with lower gradient (about $\frac{1}{2}$ ) and all points lower

B1

[Maximum number: 4]

(a)

Two sources $\mathrm{S}_{1}$ and $\mathrm{S}_{2}$ of sound waves are positioned as shown in Fig. 5.2.

Fig. 5.2 (not to scale)

The sources emit coherent sound waves of wavelength 0.85 m . A sound detector is moved parallel to the line $S_{1} S_{2}$ from a point X to a point Y. Alternate positions of maximum loudness L and minimum loudness Q are detected, as illustrated in Fig. 5.2.

Distance $S_{1} X$ is equal to distance $S_{2} X$ . Distance $S_{2} Y$ is 7.40 m.

[ 4 ]

(i)

Explain what is meant by coherent waves.

[ 1 ]

(ii)

State the phase difference between the two waves arriving at the position of minimum loudness Q that is closest to point X.
phase difference =

[ 1 ]

$180^{\circ}$

A1

(iii)

Determine the distance $S_{1} Y$ .
distance = m

[ 2 ]

path difference $=2 \lambda$ or $\mathrm{S}_{1} \mathrm{Y}-\mathrm{S}_{2} \mathrm{Y}=2 \lambda$

C1

$\begin{aligned} \text { distance } =7.40+(0.85 \times 2) =9.1 \mathrm{~m} \end{aligned}$

A1

All question bank results loaded

Covered syllabus points

8. Superposition question 1

Question (a)

Question (i)

Question (ii)

8. Superposition question 2

Question (a)

Question (i)

Question (ii)

Question (i)

Question (ii)

Question (b)

Question (i)

Question (ii)

8. Superposition question 3

Question (a)

Question (i)

Question (ii)

Question (iii)