A searchlight rotates at a rate of 2 revolutions per minute. The beam hits a wall located 11 miles away and produces a dot of light that moves horizontally along the wall. How fast (in miles per hour) is this dot moving when the angle $\theta$ between the beam and the line through the searchlight perpendicular to the wall is $\frac{\pi}{3}$? Note that $d\theta/dt=2(2\pi)=4\pi$.

Speed of dot = mph.