If two waves, each of amplitude #z#, produce a resultant wave of amplitude #z#, then what is the phase difference between them? Is there a specific equation or formula I can use?
Seems like the phase difference is between 0 and 180 because 0 (inphase) would imply a resultant of 2z and 180 would give a resultant of 0.....
Seems like the phase difference is between 0 and 180 because 0 (inphase) would imply a resultant of 2z and 180 would give a resultant of 0.....
1 Answer
For the amplitude of the superposition of two waves to have the same amplitude as the original waves, their phase difference must be
Explanation:
Consider the superposition of two sinusoidal waves of identical amplitude
The mathematical expressions for the waves
The mathematical expression for the superposition of these two waves is :
This shows that the superposition is another sinusoidal wave of amplitude
This amplitude is the same as
Derivation of the expression for the superposition of two waves:
Use the trigonometric identity (TI3) to expand
Use trigonometric identity (TI1) to rewrite the
Use the trigonometric identity (TI3) again to simplify the terms inside the square bracket
Useful trigonometric identities: