IBDP Physics 4.3 – Wave characteristics: IB Style Question Bank SL Paper 2

a.

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»