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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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