b
(b)

Apparent frequency of sound heard by the observer from source is

\(n_1=\left(\frac{v-v_0}{v-v_s}\right) n\)

\(=\left(\frac{v-u}{v+v_s}\right) n\)

Apparent frequent of sound heard by the observe from source

\(n _2=\left(\frac{ v + v _0}{ v - v _0}\right) n\)

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

\(\text { No. of beats }=8\)

\(n _2- n _{ l }=8\)

\(\left(\frac{ v + u }{ v - v _{ s }}\right) n -\left(\frac{ v - u }{ v + v _{ s }}\right) n =8 \quad v =300, v _{ s }=0, n =660\)

\(\Rightarrow\left(\frac{330+ u }{300-0}\right)(600)-\left(\frac{300- u }{330+0}\right) 660=8\)

\(\therefore \frac{2 \times 6604}{330}=8\)

\(4 u =8\)

\(u =2 .\)