# How to calculate the intensity of the interference of two waves in a given point?

There are two different point sources which produce spherical waves with the same power, amplitude, ω, wavenumber and phase.

I can calculate the intensity of each wave in a point: $$I_1 = P / (4 \pi r_1^2)$$ $$I_2 = P / (4 \pi r_2^2)$$ But how can I calculate the intensity of the resulting wave in that point?

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Are the sources at the same point or seperated? Where are you trying to find the intesity? –  Michael Brown Feb 20 at 21:04
@MichaelBrown The sources are separated. And I want to find the intensity in a point where there is constructive interference (but I'm curious about finding the intensity in a random point too) –  Oriol Feb 20 at 21:19
Well then you just need to add the two amplitudes together and square that. It's important that you add the amplitudes, not the intensities. Formula for spherical waves can be found here en.wikipedia.org/wiki/Wave_equation#Spherical_waves –  Michael Brown Feb 20 at 21:34
@MichaelBrown Why? I don't understand wikipedia article –  Oriol Feb 20 at 22:10
Waves add by their amplitudes, not their intensities. Otherwise there would be no interference. The amplitude for a general spherical wave is given in the article. For a pure (single frequency) wave it can be written $A \cos(k r - \omega t)/r$ where $k$ is the wavenumber, $r$ is the distance from the source, $\omega$ is the frequency, $t$ is the time and $A$ is the overall scale of the amplitude (loud or quiet etc.). You have one of these expressions for each source and you must add them together. This gives the amplitude at any point in space. You square that to get the intensity. –  Michael Brown Feb 20 at 23:00