Overall Intensity of Destructively Interfering Waves

[JSGandora]

If you have two sound sources emitting the same frequency and in phase with each other such that the emitted waves destructively interfere along the line containing the two sources, is the intensity at the points 0 or the sum of the intensity of each source independently?

 

[Khashishi]

zero

 

[Simon Bridge]

You can check this from the definition of "intensity" - it is proportional to the square of the amplitude.
If the amplitude is zero then the intensity must be zero.

 

[dauto]

Also note that the waves might interfere destructively along a line that passes between the two sound sources, not along a line that connects the sources. Along that second line you'll form a standing wave.