MHTCET 15 May 2024 Shift 1 Paper

Concept:This question is based on the Doppler effect, applied in two stages using the wall as a reflector.Explanation:The car is the source of sound and moves toward the stationary wall.So, the wall first acts as a stationary observer receiving the siren frequency.Using the Doppler formula for a moving source toward a stationary observer:$$f_{\text{wall}} = \frac{V}{V - V_1} n$$Here, $V$ is the speed of sound, $V_1$ is the car's speed, and $n$ is the actual siren frequency.Now, the wall reflects this sound and acts as a stationary source of frequency $f_{\text{wall}}$.The driver moves toward this stationary source, so the observed frequency increases.Using the Doppler formula for a moving observer toward a stationary source:$$f_{\text{heard}} = \frac{V + V_1}{V} f_{\text{wall}}$$Substitute $f_{\text{wall}}$ into this equation:$$f_{\text{heard}} = \frac{V + V_1}{V} \times \frac{V}{V - V_1} n$$Simplifying gives:$$f_{\text{heard}} = \frac{V + V_1}{V - V_1} n$$Answer:The frequency of the reflected sound heard by the driver is $\left(\frac{V + V_1}{V - V_1}\right) n$ Hz.This corresponds to Option A.