Fundamental frequency of sonometer wire is n . If length, tension and diameter of wire are tripled,

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14.Waves and Sound

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Fundamental frequency of sonometer wire is $n$. If the length, tension and diameter of wire are tripled, the new fundamental frequency is

A

$\frac{n}{{\sqrt 3 }}$

B

$\frac{n}{3}$

C

$n\sqrt 3 $

D

$\frac{n}{{3\sqrt 3 }}$

Solution

(d) $n = \frac{1}{{2l}}\sqrt {\frac{T}{{\pi {r^2}\rho }}}$

$\Rightarrow n \propto \frac{{\sqrt T }}{{lr}}$

==> $\frac{{{n_1}}}{{{n_2}}} = \sqrt {\frac{{{T_1}}}{{{T_2}}}} \times \frac{{{l_2}}}{{{l_1}}} \times \frac{{{r_2}}}{{{r_1}}}$

$ = \sqrt {\frac{T}{{3T}}} \times \frac{{3l}}{l} \times \frac{{2r}}{r} = 3\sqrt 3 $

==> ${n_2} = \frac{n}{{3\sqrt 3 }}$

Standard 11

Physics

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(JEE MAIN-2023)