A wire of length $30\,cm$, stretched between rigid supports, has it's $n^{\text {th}}$ and $(n+1)^{\text {th}}$ harmonics at $400\,Hz$ and $450\; Hz$, respectively. If tension in the string is $2700\,N$, it's linear mass density is.........$kg/m$.
JEE MAIN 2022, Medium
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$\frac{ nv }{0.6}=400 \& \frac{( n +1) v }{0.6}=450$
$\left[\frac{0.6 \times 400}{ v }+1\right] \frac{ v }{0.6}=450$
$= v =30$
$\sqrt{\frac{ T }{\mu}}=30$
$\frac{2700}{\mu}=900=\mu=3$
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