Two microwave transmitters, X and Y, are placed 12 cm apart and are connected to the same source. A single receiver is placed 54 cm away and moves along a line AB that is parallel to the line joining X and Y.

Maxima and minima of intensity are detected at several points along AB.

(i) Explain the formation of the intensity minima.

(ii) The distance between the central maximum and the first minimum is 7.2 cm. Calculate the wavelength of the microwaves.

Radio waves are emitted by a straight conducting rod antenna (aerial). The plane of polarization of these waves is parallel to the transmitting antenna.

An identical antenna is used for reception. Suggest why the receiving antenna needs to be be parallel to the transmitting antenna.

The receiving antenna becomes misaligned by 30° to its original position.

The power of the received signal in this new position is 12 μW.

(i) Calculate the power that was received in the original position.

(ii) Calculate the minimum time between the wave leaving the transmitting antenna and its reception.

i
minima = destructive interference
Allow “crest meets trough”, but not “waves cancel”.
Allow “destructive superposition” but not bald “superposition”.

at minima waves meet 180° or π out of phase
Allow similar argument in terms of effective path difference of \(\frac{\lambda }{2}\).
Allow “antiphase”, allow “completely out of phase”
Do not allow “out of phase” without angle. Do not allow \(\frac{{n\lambda }}{2}\) unless qualified to odd integers but accept \(\left( {n + \frac{1}{2}} \right)\lambda \)

ii
\(\lambda  = \frac{{sd}}{D}\) or \(\lambda  = \frac{{12 \times 2 \times 7.2}}{{54}} = \) or \(\lambda  = \frac{{12 \times 7.2}}{{54}} = \) seen
Award [2] for a bald correct answer.

\(\lambda  = \) «\(\frac{{12 \times 2 \times 7.2}}{{54}} = \)» 3.2 «cm»
Award [1 max] for 1.6 «cm»
Award [2 max] to a trigonometric solution in which candidate works out individual path lengths and equates to \(\frac{\lambda }{2}\).

ALTERNATIVE 1

the component of the polarized signal in the direction of the receiving antenna

is a maximum «when both are parallel»

ALTERNATIVE 2:

receiving antenna must be parallel to plane of polarisation
for power/intensity to be maximum

Do not accept “receiving antenna must be parallel to transmitting antenna”

ALTERNATIVE 3:

refers to Malus’ law or  I = I₀ cos²θ

explains that I is max when θ = 0

ALTERNATIVE 4:

an electric current is established in the receiving antenna which is proportional to the electric field

maximum current in receiving antenna requires maximum field «and so must be parallel»

i
\({I_0} = \frac{I}{{{{\cos }^2}\theta }}\) or \(\frac{{12}}{{{{\cos }^2}30}}\) seen
Award [2] for bald correct answer.
Award [1 max] for MP1 if 9 x 10^-6W is the final answer (I and I₀ reversed).
Award [1 max] if cos not squared (14 μW).

1.6 × 10^-5«W»
Units not required but if absent assume W.

ii
1.9 × 10^–4 «s»