Question

You are standing 2.5 m directly in front of one of the two loudspeakers shown in the figure. they are 3.0 m apart and both are playing a 686 hz tone in phase

Answer 1

I'll just find out the path difference between the waves at the starting point. At infinity, the path difference will be zero because the observer will be infinitely far away from both. As the observer goes farther, the path difference keeps reducing till it reaches zero as the observer reaches infinity. 
Path difference at starting point = Distance from lower speaker - Distance from upper speaker = √((3)² + (2.5)²) - 2.5 = 1.405 m 
Now to find wavelength. 
Speed of sound in air at 20 degrees C = 343 m/s 
Wavelength = 343 / 686 = 0.5 m 
Destructive interference occurs when path difference = (2n + 1)λ/2 where n is an integer. 
Maximum n possible can be found by, 
(2n + 1)λ/2 < 1.405 
(2n + 1) < (1.4)(2) / (0.5) 
2n < 5.6 - 1 
2n < 4.6 
n < 2.3 
So, we have 3 values of n, 0, 1 and 2. 
Path differences are, λ/2, 3λ/2 and 5λ/2 which have values 0.25 m , 0.75 m and 1.25 m 
But the question asks for distance from starting point. (sheesh!!) 
Lets say the observer walked x distance. 
Path difference = √((3)² + (2.5 + x)²) - (2.5 + x) 
Equate this expression to the values obtained above to get the different values of x.