Answer
${\bf 85}\;\rm m $
Work Step by Step
When two sound waves of slightly different frequencies are superimposed, they produce a beat frequency, and the distance over which one beat occurs is the length of one wave packet.
The beat frequency is given by
$$ f_{\rm{beat}} = f_2 - f_1 \tag 1$$
The length $ \Delta x $ of one wave packet is given by
$$ \Delta x = \frac{v}{f_{\rm{beat}}} $$
where $ v $ is the speed of sound in air.
Plug from (1);
$$ \Delta x = \frac{v}{ f_2 - f_1} $$
Plug the known;
$$ \Delta x = \frac{340}{ (502 - 498) }=\color{red}{\bf 85}\;\rm m $$
Thus, the length $\Delta x$ of one wave packet is 85 m.
