GS-2 Physical Sciences Question 29

[dnpgr16513]

Can someone clarify this more? I'm still confused....



THANKS

[jellywing_2058]

Let us say the amplitudes are A1 and A2.
When they are out of phase by pi, then destructive interference occurs; the crest of one is at the trough of the other and the resulting amplitude is A2 – A1 = 4, the minimum possible.

When the two are in phase, then constructive interference occurs; the crest of one is at the crest of the other and the resulting Amplitude is A2 + A1 = 12, the maximum possible.

Therefore,
A2 – A1 = 4
A2 + A1 = 12

On Adding:
2 A2 = 16
A2 = 16/ 2 = 8

And,
A1 = 12 – A2 = 12 – 8 = 4

The possible amplitudes are thus
Correct Choice B: 8 and 4 units.

The difference must be 4 and the sum must be 12 units.

Choice A: 6 and 2 units.
Difference is 4 units, but the sum is 8, not 12 units.

Choice D: 10 and 2 units.
Sum is 12 units, but the difference is 8 units and not 4.

Choice C: 12 and 4
Difference is 8, not 4; and sum is 16, not 12.

[dnpgr16513]

Ok, makes a lot more sense. Thanks!