Answer
The beat frequency is $2.6 ~Hz$
Work Step by Step
(a) We can find the frequency detected from the speaker the person is approaching.
$f' = (1+\frac{v_{obs}}{v_{snd}})~f$
$f' = (1+\frac{1.6~m/s}{343~m/s})~(282~Hz)$
$f' = 283.3~Hz$
We can find the frequency detected from the speaker that the person is moving away from.
$f' = (1-\frac{v_{obs}}{v_{snd}})~f$
$f' = (1-\frac{1.6~m/s}{343~m/s})~(282~Hz)$
$f' = 280.7~Hz$
The beat frequency is the difference in the two frequencies which are detected. The beat frequency is $283.3~Hz-280.7~Hz$ which is $2.6 ~Hz$.