Destructive interference near two speakers

[help I have 12 hours]

Homework Statement

Two acoustic speakers face each other at opposite ends of a 50.0 m walkway. The speakers broadcast an identical, 66 Hz sound wave in phase. Consider a person walking along x, the straight line from one speaker to the other.

Calculate the shortest distance from the face of either speaker to a position where destructive interference causes the sound to become weak. Show your work here, and then enter your final numeric answer in the next answer box.

Relevant Equations

change in path distance=wave length*(m+0.5)
v sound=343 m/s

where x is the distance from one speaker
343=(66)(5.197)
wave length =5.197m
x-(50-x)=(5.197)(m+0.5)
I choose m=-10

2x-50=(5.197)(-9.5)

x=0.314m?

Prof says correct answer is 1.6m tho

 

[mfb]

Working with units and formulas would make it easier to understand what you do.

x=0.314 m away from the speaker the distance difference is 50m-2*x = 49.382m, that is 9.502 times the wavelength. Looks good.

Was the speed of sound part of the problem statement? Assuming a different number here changes the result a lot. 325 m/s would lead to the answer of the professor. That value is a bit on the low side, but not impossible.