the answer for the path length difference is 073m but how do

the answer for the path length difference is 0.73m but how do I know whether it is constructive, deconstructive, or neither? Please explain and show work thank you so much!

Sound Interference Two loudspeakers are 2.0 m apart and are driven by the same oscillator. Both speakers emit 700 Hz sound waves into a room where the speed of sound is 341 m/s o m A listener stands 5.0 m 700 Hz in front of the speakers and 2.0 m to one side of the center. Does the 1.0 m listener experience constructive interference, destructive interference, or neither at this location? 2.0 m 2 1.0 m 700 Hz Copyrigh 2008 Peerson Eduebionpublishing as Pearson Adosony

Solution

f = 700 Hz and v = 341 m/s

and lambda = v / f = 341/700 = 0.487 m

and path difference = r2 - r1

= sqrt[5^2 + 3^2] - sqrt[5^2 + 1^2]

= 0.732 m

constructive interference if path diff = m*lambda

destructive, if path diff = (m+0.5)*lambda

where m = 0,1,2,3,....

0.732 = n (0.487)

n = 1.5 = 1 + 0.5

hence destructive interfarance