c
For \(1^{st}\) source

\(n _{1}= n \left(\frac{ v - u }{ v }\right)=\left(1-\frac{ u }{ v }\right) n\)

for \(2^{nd}\) source

\(n _{2}= n \left(\frac{ v + u }{ v }\right)=\left(1+\frac{ u }{ v }\right) n\)

Beat freq. \(=\left| n _{1}- n _{2}\right|= n +\frac{ nu }{ v }- n +\frac{ nu }{ v }\)

\(=\frac{2 nu }{ v }=2 \frac{ u }{\lambda}\left[\because v = n \lambda \quad \therefore \frac{1}{\lambda}=\frac{ n }{ v }\right]\)