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(D) For the echo to not be heard distinctly,the time interval between the drum beats must be equal to the time taken for the echo to return.Let $d$ be

Vedclass · Accepted Answer

$270$

Vedclass · Answer

(D) For the echo to not be heard distinctly,the time interval between the drum beats must be equal to the time taken for the echo to return.Let $d$ be the initial distance and $v$ be the speed of sound.The time interval for $40$ beats per minute is $t_1 = \frac{60}{40} = 1.5 \ s$.Thus,$\frac{2d}{v} = 1.5 \implies 2d = 1.5v$......$(i)$When the man moves $90 \ m$ closer,the new distance is $(d - 90) \ m$.The time interval for $60$ beats per minute is $t_2 = \frac{60}{60} = 1 \ s$.Thus,$\frac{2(d - 90)}{v} = 1 \implies 2d - 180 = v$......$(ii)$Substituting $2d = 1.5v$ from equation $(i)$ into equation $(ii)$:$1.5v - 180 = v$$0.5v = 180 \implies v = 360 \ m/s$.Now,substituting $v = 360 \ m/s$ back into equation $(i)$:$2d = 1.5 	imes 360 = 540$$d = 270 \ m$.

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