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Q. Determine the amplitude and phase of the resultant motion when two sinusoidal motions having the same frequency and traveling in the same direction are combined, if their amplitudes are 3.0cm and 4.0cm, and they differ in phase by pi/2 radians.

We have been covering wave interference, and how they either constructively or destructively interfere.

What I believe I need to find the new amplitude is:

A'= sqrt(A1^2 + A2^2 + 2*A1*A2*cos(phi2 - phi1))

Letting A1=4, A2=3, phi1=0 and phi2= pi/2 radians

Then I calculate A' as 5cm. I think this is correct. In fact, I graphed the sum of the two equations, Y3 = Y1+Y2 and the max amplitude verifies as 5cm.

Now I am having trouble with the phase.

I am trying to use:

tan(phi3) = (A1*sin(phi1) + A2*sin(phi2)) / (A1*cos(phi1) + A2*cos(phi2))

Using the same assignments above for the A1, A2 etc...

tan(phi3) = (4sin(0) + 3sin(pi/2)) / (4cos(0) + 3cos(pi/2))

tan(phi3) = (0 + 3) / (4 + 0)

phi3 = arctan(3/4)

phi3 = .643501pi radians ?

Is this correct? Am I writing this wrong? I know this is basic, but I am blanking out, and having trouble here.

Also, the text we are using does not address the superposition of two waves with different amplitudes and a phase shift. The prof's notes are impossible for me to follow. I even broke out my precalc text, and only confused myself further.

Please help.

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# Homework Help: Superposition of 2 waves problem

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