MHTCET 11 Apr 2026 Shift 2 Paper

Concept:When a sound source moves relative to a stationary observer, the observed frequency changes due to the Doppler effect.Explanation:When the source moves towards the observer with speed $V_S$, the apparent frequency is:$$n_1 = n\left(\frac{V}{V - V_S}\right)$$When the source moves away from the observer with speed $V_S$, the apparent frequency is:$$n_2 = n\left(\frac{V}{V + V_S}\right)$$The required difference is:$$n_1 - n_2 = n\left(\frac{V}{V - V_S}\right) - n\left(\frac{V}{V + V_S}\right)$$Taking $nV$ common and simplifying:$$n_1 - n_2 = nV\left(\frac{1}{V - V_S} - \frac{1}{V + V_S}\right)$$$$= nV\left(\frac{(V + V_S) - (V - V_S)}{V^2 - V_S^2}\right)$$$$= nV\left(\frac{2V_S}{V^2 - V_S^2}\right)$$Therefore, the difference between the apparent frequencies is:$$\frac{2nVV_S}{V^2 - V_S^2}$$Answer:Option A: $\frac{2 n V V_{s}}{V^{2}-V_{s}^{2}}$