A wire of length 30,cm , stretched between rigid supports, has it's n^{text {th}} and (n+1)^{tex

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14.Waves and Sound

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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.........$kg/m$.

A

$1.5$

B

$6$

C

$9$

D

$3$

(JEE MAIN-2022)

Solution

$\frac{ nv }{0.6}=400 \& \frac{( n +1) v }{0.6}=450$

$\left[\frac{0.6 \times 400}{ v }+1\right] \frac{ v }{0.6}=450$

$= v =30$

$\sqrt{\frac{ T }{\mu}}=30$

$\frac{2700}{\mu}=900=\mu=3$

Standard 11

Physics

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