MHTCET 23 Apr 2025 Shift 2 Paper

Concept:Doppler effect for sound when both source and observer are in motion relative to each other.Explanation:The apparent frequency is given by $f' = F \cdot \frac{v \pm v_o}{v \mp v_s}$.Here, $v$ = velocity of sound, $v_o$ = velocity of observer, and $v_s$ = velocity of source.The observer moves away from the source, so the observed frequency decreases. Therefore, the numerator becomes $v - v_o$.The source moves towards the observer, so the observed frequency increases. Therefore, the denominator becomes $v - v_s$.Given $v_o = \frac{V}{4}$ and $v_s = \frac{V}{3}$.Substituting these values gives $f' = F \cdot \frac{V - \frac{V}{4}}{V - \frac{V}{3}}$.Simplifying the numerator: $V - \frac{V}{4} = \frac{3V}{4}$.Simplifying the denominator: $V - \frac{V}{3} = \frac{2V}{3}$.Thus, $f' = F \cdot \frac{\frac{3V}{4}}{\frac{2V}{3}} = F \cdot \frac{3V}{4} \cdot \frac{3}{2V} = \frac{9}{8}F$.Answer:The apparent frequency heard by the observer is $\frac{9}{8}F$.Hence, the correct option is Option A.