Superposition, amplitudes and superposed waves.

isabelle87

First off:
Sorry. I'm a Norwegian girl, so my English may not be of very good quality.
Now that's said...

I have this problem to solve.
Only thing is - I don't have a clue how!
I'm no good at physics, but unfortunately I have to have this class.

Anyway.
My problem is this:

Task 1a)
Two harmonic waves are mutually coherent.
One wave has an intensity of 4 unit^2,
the other wave has the intensity of 9 unit ^2,
their superposition wave will have an amplitude of

Task 1b)
Two waves are mutually incoherent.
One wave has an amplitude of 3 unit,
the other wave has an amplitude of 4 unit.
The intensity for the superposed wave should be?

How do I calculate this?
What formula am I suppose to use?
And if you only wan't to give me the formula,
can you please explain what the different letters, symbols and stuff means (so that I can solve it myself, if you don't want to give me the direct answer?)

vertices

hmmm

1a)the intensity is propotional to the amplitude squared. if they're mutually coherent you add the amplitudes and square the resultant (ans= 25 unit^2 i think)

1b)if mutually incoherent, there's a phase difference. so for all you know, a peak of one wave could coincide with a trough of the other. The resultant amplitude is anywhere from 1 to 7 (ie. intensity=1 to 49)

isabelle87

Thank you for your reply, but did you perhaps overlook that it said "9 unit^2"?

Anyway.
If I now do this your way it'll be like this rigth?
9^2 + 4^2 = 97
And you believed I should square the result so that the final answer would be 97^2.

I don't know if this is right,
but either way I'm really thankful for your advice/opinion.
It's certainly worth a try!

:D

isabelle87

The second answer you gave me seems to be wrong,
I found out to crack it on my own.
Or... At least i think I did ;)

Because the waves are incoherant I have to use the formula:
I = I1 + I2
= 3^2 + 4^2
= 25

The intensity for the superposed wave should be 25.

vertices

^^ Not sure if that's correct TBH.

I(total) is infact I1+I2+(A1*A2)cos(X)

where X is the phase difference between the two waves and A is the amplitude. Incoherent waves, by definition, have a difference in phase.