CAIE A-Level Physics 8.1.1 Principle of Superposition

Practise applying superposition by adding instantaneous displacements, calculating or sketching resultants and explaining interference or stationary waves.

Exam points

state and apply the principle of superposition by adding the instantaneous displacements of overlapping waves
calculate or sketch resultant displacement, amplitude or intensity from component waves, including phase difference
use superposition to explain constructive and destructive interference or the formation of a stationary wave

[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

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8.1.1—And use the principle of superposition question 1

Question (a)

Question (i)

Question (ii)