Answer
a) $x=0.265m$
b) Now, the maxima and minima will be switched. The intensity minima is at midpoint and the intensity maxima are at $0.265m$ to the left and right.
Work Step by Step
a) $d_2-d_1=\frac{\lambda}{2}$
$\lambda=\frac{v}{f}=\frac{343\frac{m}{s}}{474Hz}=0.724m$
$\sqrt{(3.00m+x)^2+(3.20m)^2}-\sqrt{(3.00m-x)^2+(3.20m)^2}=\frac{0.724m}{2}$
$\sqrt{19.24m^2+6.00mx+x^2}-\sqrt{19.24m^2-6.00mx+x^2}=0.362m$
$19.24m^2+6.00mx+x^2=19.24m^2-6.00mx+x^2+0.131m^2+0.724m\sqrt{19.24m^2-6.00mx+x^2}$
$138x^2+43.7x-154=0$
$x=0.265m$
b) Now, the maxima and minima will be switched. The intensity minima is at midpoint and the intensity maxima are at $0.265m$ to the left and right.
