Paper 2 Superposition of Waves Answers

Q1 Young double-slit fringes

1. Sources must be coherent, have the same frequency/wavelength, and have comparable amplitudes. [2]
2. $x=\lambda D/a$, so $\lambda =xa/D=(2.90\times 10^{-3})(0.420\times 10^{-3})/1.80=6.77\times 10^{-7}\mathrm{m}$. [3]
3. Fringe spacing increases because $x\propto D$. [1]
4. Waves arrive with different path differences. Integer-wavelength path differences give constructive interference and bright fringes; half-integer path differences give destructive interference and dark fringes. [3]

Q2 Stationary wave on a string

1. Three loops. [1]
2. For $n=3$, $L=3\lambda /2$, so $\lambda =2L/3=0.600\mathrm{m}$. [2]
3. $v=f\lambda =180(0.600)=108\mathrm{m}{\mathrm{s}}^{-1}$. [2]
4. The incident and reflected waves have equal frequency and speed and travel in opposite directions. At nodes, destructive superposition occurs at all times, so displacement remains zero. [2]

Q3 Diffraction grating

1. $d=1/(600\times 10^3)=1.67\times 10^{-6}\mathrm{m}$. [2]
2. $d\sin \theta =\lambda$, so $\sin \theta =520\times 10^{-9}/1.67\times 10^{-6}=0.312$, giving $\theta =18.2^{\circ }$. [2]
3. For $n=3$, $\sin \theta =3\lambda /d=0.936<1$, so the third order is possible. [2]