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14.Waves and Sound
medium
A string is stretched so that its length is increased by $\frac{1}{\eta }$ of its original length. The ratio of fundamental frequency of transverse vibration to that of fundamental frequency of longitudinal vibration will be
A
$\eta :1$
B
$1:\eta $
C
$\sqrt \eta :1$
D
$1:\sqrt \eta $
Solution
$\frac{{{{\rm{f}}_T}}}{{{{\rm{f}}_\ell }}} = \sqrt {\frac{{\frac{{\rm{T}}}{\mu }}}{{\frac{{\rm{r}}}{{\rm{s}}}}}} = \sqrt {\frac{{\frac{{\rm{T}}}{{\rho {\rm{A}}}}}}{{\frac{{{\rm{T}}\ell }}{{\rho {\rm{A}}\Delta \ell }}}}} = \sqrt {\frac{{\Delta \ell }}{\ell }} = \frac{1}{{\sqrt \eta }}$
Standard 11
Physics
