Paper 3 Superposition of Waves Answers

Q1 Two-source interference in water

1. Path difference $=22.5-18.0=4.5\mathrm{cm}$. [1]
2. $4.5/1.5=3$, so the path difference is $3\lambda$ and interference is constructive. [2]
3. Coherent sources maintain constant phase difference, so positions of maxima and minima remain fixed rather than drifting with time. [2]
4. Larger wavelength gives larger angular spacing between adjacent nodal/antinodal lines. [2]
5. Destructive interference means resultant displacement is reduced at that point. The individual waves still carry energy through the region, and energy appears in neighbouring constructive regions; it is redistributed in space, not destroyed. [3]

Q2 Single-slit and grating comparison

1. $a\sin \theta =\lambda$, so $\sin \theta =630\times 10^{-9}/0.18\times 10^{-3}=3.50\times 10^{-3}$ and $\theta =0.201^{\circ }$. [2]
2. $d\sin \theta =\lambda$, so $\sin \theta =630\times 10^{-9}/2.0\times 10^{-6}=0.315$ and $\theta =18.4^{\circ }$. [2]
3. A single slit has continuous contributions across one aperture, producing a broad diffraction envelope. A grating has many regularly spaced slits, so constructive interference only occurs sharply at angles satisfying the grating condition. [3]
4. The bright maxima are sharp and their angles satisfy $d\sin \theta =n\lambda$, allowing precise wavelength determination. [2]