Two loudspeakers placed next to each other each emit a pure tone with the same amplitude. One speaker emits a tone with a frequency of $473\mathrm{.}0$ Hz$,$ the other with a frequency of $480\mathrm{.}0$ Hz$.$

A distant listener perceives a pure tone that has a single frequency, but varies in loudness with a perceived "beat."

$($a$)$

What is the frequency $($in Hz$)$ of the pure tone perceived by the listener? $($Round your answer to at least the nearest integer.$)$

Hz

$($b$)$

What is the beat frequency $($in Hz$)$ perceived by the listener?

Hz