If the tension and diameter of a sonometer wire of fundamental frequency n is doubled and density is halved then its fundamental frequency will become

Waves question

2001 · Q166

Waves question

2001 · Q166

View written solutionFree

Correct answer: C

$n = {1 \over {2l}}\sqrt {{T \over {\pi {r^2}\rho }}}$

$\rho _1^{'} = {\rho \over 2};T' = 2T$

D' = 2D or r' = 2r

$n' = {1 \over {2l}}\sqrt {{{2T} \over {\pi {{\left( {2r} \right)}^2}{\rho \over 2}}}}$

After solving, $n' = {1 \over {2l}}\sqrt {{{2T} \over {\pi {r^2}l}}} = n$

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Waves question

2001 · Q166

Waves question

2001 · Q166

View written solutionFree

Correct answer: C

$n = {1 \over {2l}}\sqrt {{T \over {\pi {r^2}\rho }}}$

$\rho _1^{'} = {\rho \over 2};T' = 2T$

D' = 2D or r' = 2r

$n' = {1 \over {2l}}\sqrt {{{2T} \over {\pi {{\left( {2r} \right)}^2}{\rho \over 2}}}}$

After solving, $n' = {1 \over {2l}}\sqrt {{{2T} \over {\pi {r^2}l}}} = n$