Why Is the Resultant Amplitude of Interfering Waves Not Simply A1 + A2?

[desmond iking]

Homework Statement

when a point is intefered by 2 waves of different phase , the resultant is y1 + y2 ... but why the resultant amplitude can't be = A1 + A2 ... but is sqrt root ((A1)^2 + (A2)^2) ??

this is actually a online note.

Homework Equations

The Attempt at a Solution

 

[NascentOxygen]

when a point is intefered by 2 waves of different phase , the resultant is y1 + y2 ... but why the resultant amplitude can't be = A1 + A2 ... but is sqrt root ((A1)^2 + (A2)^2) ??

It isn't, and your pic shows it isn't. The peak of the resultant amplitude is determined using the cosine rule and the phase angle difference. Only if the phase angle was 90 degrees would your equation using Pythagoras hold.

 

[desmond iking]

It isn't, and your pic shows it isn't. The peak of the resultant amplitude is determined using the cosine rule and the phase angle difference. Only if the phase angle was 90 degrees would your equation using Pythagoras hold.

sorry, i mean why can't i add up A1 and A2 to get the resultant amplitude... tHat means resultant amplitude =A1+ A2

 

[dauto]

Because y₁ and y₂ never reach their maximum values at the same time. unless they're in phase (θ = 0).