For a certain organ pipe, the first three resonance frequencies are in the ratio of $1:3:5$ respectively. If the frequency of fifth harmonic is $405\,Hz$ and the speed of sound in air is $324 \,ms ^{-1}$ the length of the organ pipe is $..........m.$
A$0$
B$2$
C$3$
D$1$
JEE MAIN 2023, Medium
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D$1$
d For $5^{\text {th }}$ harmonic in closed organ pipe,
$f _5=\frac{5 V }{4 \ell} \Rightarrow 405=\frac{5 \times 324}{4 \ell}$
$\Rightarrow \ell=1 \,$
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