A $1024$ Hz tuning fork is dangled at the end of a string such that its center of mass is $1\mathrm{.}2$ m below the point at which the other end of the string is attached to door frame, making a pendulum of sorts. The tuning fork may be treated as a point mass for the purposes of this problem. If the pendulum is brought to an amplitude of $22$ and released, what is the range of frequencies heard by an observer standing in the plane of the pendulum's motion? The speed of sound is $340\frac{m}{s}.$