Question

When i stand halfway between two speakers, with one on my left and one on my right, a musical note from the speakers gives me constructive interference. how far to my left should i move to obtain destructive interference?

Answer 1

Destructive interference occurs when the difference is π, 3π, 5π ..., whereas constructive interference occurs when the phase difference between the waves is a multiple of 2π. 
If the difference between the phases is intermediate between these two extremes, then the magnitude of the displacement of the summed waves lies between the minimum and maximum values. 

One wavelength is equal to 2π (360°) and 1/2 wavelength is equal to π (180°). 

so Half a Wavelength.

Answer 2

Answer: B. Half a wavelength

Explanation:

When i stand halfway between two speakers, with one on my left and one on my right, a musical note from the speakers gives me constructive interference. how far to my left should i move to obtain destructive interference?

a. One-fourth of a wavelength

b. Half a wavelength

c. One wavelength

d. One and half a wavelengths

e. Two wavelengths

Destructive interference occurs when the right speaker is half a wavelength further away than the left. Let "d" represents distance from each speaker to the me, the listener. To achieve destructive interference, I would have to calculate the distance in terms of wavelength as thus:

(d + wavelength/4) - (d - wavelength/4) = half a wavelength/4

Put in a different term, the path difference must be half a wavelength. Whatever that amount is, you can achieve this path difference by moving half that amount.