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14.Waves and Sound
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The fundamental frequency of a sonometre wire is $n.$ If its radius is doubled and its tension becomes half, the material of the wire remains same, the new fundamental frequency will be
A
$n$
B
$\frac{n}{{\sqrt 2 }}$
C
$\frac{n}{2}$
D
$\frac{n}{{2\sqrt 2 }}$
Solution
(d) $n = \frac{1}{{2l}}\sqrt {\frac{T}{{\pi {r^2}\rho }}} $
==> $n \propto \frac{{\sqrt T }}{r}$
==> $\frac{{{n_2}}}{{{n_1}}} = \frac{{{r_1}}}{{{r_2}}}\sqrt {\frac{{{T_2}}}{{{T_1}}}} $
$ = \frac{1}{2} \times \sqrt {\frac{1}{2}} $=$\frac{1}{{2\sqrt 2 }}$
Standard 11
Physics
