Two coherent microwave sources X and Y, each emitting at a frequency of $2.5 \times 10^{10}\,\text{Hz}$, are separated by a gap of $0.18\,\text{m}$ in vacuum, as shown in Fig. 6.1. The two emitted waves have a phase difference of $90^\circ$. A microwave detector travels along PQ, which is parallel to the line connecting the sources and lies $2.3\,\text{m}$ from it. O lies on PQ at the point equally distant from both sources. A is the point on PQ where the microwave intensity reaches its maximum.
(a(i))[2]
Explain why the highest-intensity position is not at point O.
(a(ii))[2]
On Fig. 6.1, place a cross (x) to indicate the point on line PQ where the nearest intensity minimum to point O occurs. Name this point B.
(b(i))[2]
Show that the wavelength of the microwaves is $0.012\,\text{m}$.
(b(ii))[1]
For point A on line PQ, find the path difference $\Delta x$ between the microwaves from X and those from Y.
(b(iii))[2]
Use the double-slit interference formula to find the distance between neighbouring intensity maxima on line PQ.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “states that, for maximum intensity, the waves must be in phase at detection” …