a
The expression for beats is given by,

\(\left(F_{1}-F_{2}\right)=\left(\frac{330}{330-V}\right) \times 500-\left(\frac{330}{330+V}\right) \times 500\)

Substitute \(3\) for \(\left(F_{1}-F_{2}\right)\)

\(3=\left(\frac{330}{330-V}\right) \times 500-\left(\frac{330}{330+V}\right) \times 500\)

\(=\frac{500}{330^{2}-V^{2}} \times 2 V \times 330\)

Here \(V^{2}<<330^{2}\) so,

\(30=\frac{500 \times 330 \times 2 V}{330^{2}}\)

\(V=\frac{3}{2}\left(\frac{330}{500}\right)\)

\(\approx 1 m / s\)

Further simplify the above