MHTCET 16 Apr 2026 Shift 1 Paper

Concept:The Doppler effect for a moving observer and a stationary source changes the apparent frequency depending on the direction of the observer's motion.Explanation:When the observer moves towards the stationary source with speed $V_1$, the apparent frequency is:$$F_1 = F\left(\frac{V + V_1}{V}\right)$$When the observer moves away from the source with the same speed $V_1$, the apparent frequency becomes:$$F_2 = F\left(\frac{V - V_1}{V}\right)$$According to the given condition, $\frac{F_1}{F_2} = 2$.Substituting the expressions for $F_1$ and $F_2$:$$\frac{F\left(\frac{V + V_1}{V}\right)}{F\left(\frac{V - V_1}{V}\right)} = 2$$Cancelling the common factor $F$ and simplifying:$$\frac{V + V_1}{V - V_1} = 2$$Cross-multiplying:$$V + V_1 = 2V - 2V_1$$Bringing like terms together:$$V_1 + 2V_1 = 2V - V$$$$3V_1 = V$$Hence,$$\frac{V}{V_1} = 3$$Answer:$\frac{V}{V_1} = 3$, so the correct option is B.