Paper 4 Superposition of Waves Answers

Q1 Microwave stationary-wave measurement

1. Incident and reflected microwaves of the same frequency and similar amplitude travel in opposite directions and superpose. Fixed nodes and antinodes form. [2]
2. Axes and units [1]; suitable scale [1]; accurate plots [2]; best-fit straight line [1]. [5]

3. The best-fit gradient is approximately $1.72\mathrm{cm}$ per maximum. Adjacent maxima are separated by $\lambda /2$, so

$$\lambda =2(1.72\mathrm{cm})=3.44\mathrm{cm}=0.0344\mathrm{m}.$$

Accept follow-through from the candidate’s line. [3] 4.

$$f=\frac{c}{\lambda }=\frac{3.00\times 10^8}{0.0344}=8.72\times 10^9\mathrm{Hz}.$$

[2] 5. A best-fit gradient over several intervals reduces the percentage effect of position-reading uncertainty and random variation in locating each broad maximum. [2] 6. Move the detector slowly; minimise reflections from nearby objects; align transmitter, detector and reflector; keep detector orientation fixed; identify each maximum from approaches on both sides. Any two. [2]

Q2 Diffraction grating measurement

1. Measure grating spacing or line density, diffraction order $n$, and angle $\theta$ from central maximum to the chosen order. [2]
2. Averaging symmetric left and right angles reduces zero-offset and alignment errors. [2]
3. Grating not normal to beam, spectrometer zero error, misidentified order, or inaccurate line spacing. [1]