$(10$ points$)$ A block with a speaker bolted to it is connected to a spring having spring constant and oscillates as shown in the figure. The total mass of the block and speaker is $5\mathrm{.}0$ kg $,$ and the amplitude of this unit's motion is $0\mathrm{.}5$ m $.$ The speaker emits sound waves of frequency $440$ Hz $.$

Determine

$($a$)$ the highest and

$($b$)$ the lowest frequencies heard by the person to the right of the speaker.