Young's Double Slit Experiment Problem

[jones268]

A lecturer is demonstrating two-slit interference with sound waves. Two speakers are used, 1.9 m apart. The sound frequency is 1220Hz and the speed of sound is 343 m/s. Students sit facing the speakers in a row of sear 5.4 m away. Along the row of students, what is the spacing between the locations on either side of the center line between the speakers where no sound is heard because of destructive interference? The angle may be too large to use small angle approximation.
This is what I've come up with my known variables.
d=1.9m (Distance between the two "slits"
f=1220 Hz
c=343 m/s
L=5.4m (distance from "slits" to the "screen")
y=? unknown spacing
And I'm also assuming I'll be using the formula for dark fringe due to the fact they want
the spacing where no sound will be heard.
I've also calculated the wavelength, λ, to be 0.281147541 m from the following equation:
λ= c/f

The equation I'm using for dark fringe is as follows:
(m + 1/2)(λ)=(d)(sinθ)
Then to find the unknown y, I was using the following equation:
y=(L)(tanθ)

I'm not quite sure where to go from here and if I'm even doing this right, especially due to theta being too large to approximate.

 

[jbsteele]

The equation for dark fringe can be rearranged to solve for θ: θ = arcsin((m+1/2)*λ/d)Then you can use this expression for θ in the second equation to solve for y: y = L*tan(arcsin((m+1/2)*λ/d))Where m is the order of the dark fringe (in this case, it should be 0 since we are looking for the spacing between locations on either side of the center line). Plugging in the known variables, y = 5.4 * tan(arcsin((0 + 1/2)*0.281147541/1.9)) y = 0.358 m