Paper 3 Superposition of Waves Drills

Q1 Two-source interference in water

Two coherent water-wave sources $S_1$ and $S_2$ have separation $6.0\mathrm{cm}$ and wavelength $1.5\mathrm{cm}$. Point P is such that $S_{1}P=18.0\mathrm{cm}$ and $S_{2}P=22.5\mathrm{cm}$.

1. Calculate the path difference at P. [1]
2. Determine whether P is on a constructive or destructive line. [2]
3. Explain why the two sources must be coherent for a stable pattern. [2]
4. Describe what happens to nodal-line spacing if wavelength is increased. [2]
5. Explain why energy is redistributed rather than destroyed at destructive regions. [3]

Q2 Single-slit and grating comparison

Monochromatic light of wavelength $630\mathrm{nm}$ passes through a single slit of width $0.18\mathrm{mm}$ and then, in a separate experiment, through a grating of spacing $2.0\mu \mathrm{m}$.

1. Calculate the angle of the first single-slit minimum. [2]
2. Calculate the first-order grating angle. [2]
3. Explain why the single-slit pattern has broad maxima but the grating has sharp principal maxima. [3]
4. State one reason why a grating is useful for wavelength measurement. [2]