\(v_{2}=\left(\frac{c}{c+v}\right) v_{0}\)

beat frequency \(=v_{1}-v_{2}\)

\(=\mathrm{cv}_{0} \quad\left(\frac{1}{\mathrm{c}-\mathrm{v}}-\frac{1}{\mathrm{c}+\mathrm{v}}\right)\)

\(=c v_{0}\left(\frac{c+v-c+v}{c^{2}-v^{2}}\right)=\frac{2 c v_{0}^{2} v}{c^{2}-v^{2}}\)

\(\approx \frac{2 \mathrm{cv}_{0} \mathrm{v}}{\mathrm{c}^{2}}=\frac{2 \mathrm{v}_{0} \mathrm{v}}{\mathrm{c}}=2\)

\(\Rightarrow \frac{2 \times 1400 \times v}{350}=2\)

\(\Rightarrow \mathrm{v}=\frac{1}{4} \mathrm{m} / \mathrm{s}\)