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For mechanical waves, Is the principle of superposition valid for waves that do not travel in the same plane ? For eg with one wave S1, travels along positive x-direction and another wave S2, is travelling in a direction inclined to the x-axis at an angle of 45 degrees (both the waves have same frequency and wavelength) then will the principle of superposition apply here ? If yes then can you please explain the mathematical aspect ?

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The principle of superposition valid for waves that do not travel in the same plane. The math is the same--simple addition.

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