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.