What could be the phase difference between the two waves?
A 150°
B 220°
C 260°
D 330°
Solution:
Answer: C
The 2 light waves are said to have the same frequency. The waves have a sinusoidal form.
Let the wave with the larger amplitude be wave A and the one with smaller amplitude be wave B.
Since both waves have a sinusoidal form, we can assume that any of the 2 waves will start at displacement = 0 (we take this point as the reference point), and then move up – just like the wave A at (0, 0).
{In fact, any point (at any displacement) could be taken as the reference point, but in this question, it is easier to consider that point.}
On the graph, the x-axis gives the phase angle.
At a phase of 0°, wave B has not yet reaching the starting (reference) point while wave A is already at that point. It is only at a phase of 100° that wave B reached the reference point (or we could say that wave B reaches this point AGAIN at 100°).
The solution of 100° is not available in the 4 choices, so we can say that wave B had actually already reached this point before – we need to find at which phase this was, according to the x-axis in the diagram.
The phase angle is actually between 0° and 359°. A phase difference of 360° is the same as a phase difference of 0° and a phase difference of 1° is the same as a phase difference of 361°, ….
The wavelength of a wave corresponds to a phase difference of 360°. Since the 2 light waves have the same frequency, it means that they are the same wavelength.
So, if wave B reached the reference point again at a phase of 100°, according to the x-axis, going back by a wavelength (by a phase difference of 360°), we can say that previously, wave B had reached the reference point at the phase of
Phase = 100 – 360 = – 260°
As for wave A, it reaches the reference point at a phase of 0° (according to the x-axis).
Thus, phase difference between wave A and B = 0 – (–260) = 260°
Reference: PYQ - May/Jun 2015 Paper 12 Q24
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