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(B) The apparent frequency $F$ observed by an observer moving with velocity $v_o$ relative to a stationary source emitting frequency $f_0$ is given by

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$3$

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(B) The apparent frequency $F$ observed by an observer moving with velocity $v_o$ relative to a stationary source emitting frequency $f_0$ is given by $F = \left( \frac{V \pm v_o}{V} \right) f_0$.When the observer moves towards the stationary source with velocity $V_1$,the apparent frequency is $F_1 = \left( \frac{V + V_1}{V} \right) f_0$ $(i)$.When the observer moves away from the stationary source with velocity $V_1$,the apparent frequency is $F_2 = \left( \frac{V - V_1}{V} \right) f_0$ $(ii)$.Dividing equation $(i)$ by $(ii)$,we get $\frac{F_1}{F_2} = \frac{V + V_1}{V - V_1}$.Given $\frac{F_1}{F_2} = 2$,we have $2 = \frac{V + V_1}{V - V_1}$.Cross-multiplying gives $2(V - V_1) = V + V_1$,which simplifies to $2V - 2V_1 = V + V_1$.Rearranging the terms,we get $2V - V = 2V_1 + V_1$,which leads to $V = 3V_1$.Therefore,$\frac{V}{V_1} = 3$.

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