Question

If two waves of amplitude 'x' produce a resultant wave of amplitude 'x', phase difference between them will be
a. 0
b. 60
c. 120
d. 180 degrees

Answer 1

b

Answer 2

Um tell me how
=/

Answer 3

a. -> may be because of there may condition of constructive interferencs

Answer 4

If it's constructive interference, shouldn't the resultant amplitude be 2x?

Answer 5

The constructive interference will give give double amplitude only when both waves are exactly in phase. Let us assume that there is phase angle difference of 'theta' between the waves.

Let the first wave phasor be: x
The second phasor is: \[x <\theta = x \cos(\theta) + i x \sin(\theta)\]
The sum of this is: \[x(1+\cos(\theta)) + ixsin(\theta)\]

The amplitude of the resultant needs to be x. So, \[x*\sqrt{(1+\cos \theta)^{2}+(\sin \theta)^{2}}=x\]
Solving, we get: \[\cos \theta = -1/2\]
So, angle is 120 deg