Sound Waves-Destructive Interference hw help please

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SUMMARY

The discussion focuses on a physics homework problem involving sound waves and destructive interference between two loudspeakers positioned 5 meters apart vertically. The speakers are driven by the same source, and a detector is placed 12 meters away horizontally and 3.2 meters above the lower speaker. The objective is to determine the minimum distance the top speaker must be moved to achieve destructive interference. The velocity of sound is given as 345 m/s, and the final equation for calculating the necessary adjustments is provided but not derived by the participants.

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Homework Statement


Two loudspeakers are placed a distance of 5m above and below one another and driven by the same source. A detector is positioned a perpendicular distance of 12m from the two speakers and a vertical height 3.2m from the lower speaker. This results in constructive interference at the first order maximum. What minimum distance (in any direction0 should the top speaker be moved in order to create destructive interference between the two speakers?
*Velocity of sound=345m/s


Homework Equations


This is what the final equation comes out to be, I just don't know how to derive it.

distance apart=dA
detector placement distance=dD
detector vertical height=dH

((SQRT(dD^2+((dH-dA/2)+dA/2)^2)-(SQRT(dD^2+((dH-dA/2)-dA/2)^2)/2)

The Attempt at a Solution


I honestly have no clue how to do this or even where to start. I know the final equation and the answer, just not how to get to it. Any help is appreciated. (equation is above)
 
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I'd start with the conditions for constructive and destructive interference to happen.
 

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