Find smallest value of y for constructive interference

[hraghav]

Homework Statement

Two speakers are located a distance 2d apart along the x-axis, where the origin is located at the midpoint between the two speakers. This is shown in the image below. The speakers emit sound with wavelength λ=1.34m. The distance from the origin to either of the speakers is d=6.74m. When considering locations of constructive and destructive interference along a line parallel to the y-axis in front of one of the speakers, as shown in blue, the distance between the location and each of the speakers is R1 = y and R2 = sqrt( y^2+(2d)^2) for the right and left speakers, respectively. If a listener were a very far distance away from the speakers, the difference between the distances from the two speakers would be so small that it might as well be zero, and thus the listener would experience constructive interference.

What is the smallest value y from the right speaker in which constructive interference occurs?

Relevant Equations

\sqrt{y^2+\left(2\cdot 6.74\right)^2}\ -\ y=\ λ

I took the d = 6.74 m, n = 1 as we need the smallest y and λ=1.34m. I substituted this in the equation and am getting 67.1323 m as my final answer but this is not correct. Could someone please let me know where am I making an error

 

[BvU]

Hi,

What's the phase difference for $y=0$ ?

$\$

 

[kuruman]

Could someone please let me know where am I making an error

You asserted that $n=1$. Why does that value for $n$ give the smallest value of $y$?

 

[hraghav]

You asserted that $n=1$. Why does that value for $n$ give the smallest value of $y$?

Thanks I got it now