WHEN THE PHASE DIFFERENCE BETWEEN TWO VIBRATING SOURCES CHANGES RAPIDLY WITH TIME ,WE SAY THAT THE TWO SOURCES ARE INCOHERENT AND WHEN THAT HAPPENS THE INTENSITIES JUST ADD UP. BUT INTENSITIES ADD UP ONLY IF THE SOURCES ARE COHERENT? THEN HOW IS IT THAT INTENSITIES ADD UP WHEN THE SOURCES ARE INCOHERENT?

When the waves from the two sources interfare , the net intensity I=I0 cos²?.

 

For the incoherent sources we find the average of I beacause for incoherent sources the phase differece between the waves at a point due to two sources  vary randomly thats why we get average value of net intensity.

 

‹I›=I0‹COS²?›

‹I›=I0*1/2