QJEEM13Phe004: JEE Main 2013 Physics - Class 11 JEEM13Phe004 Solution: A sonometer wire of length is made of steel. The tension in it…

Question

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A sonometer wire of length

1.5

m

is made of steel. The tension in it produces an elastic strain of

1\%

. What is the fundamental frequency of steel if density and elasticity of steel are

7.7 \times {10^3}\,kg/{m^3}

and

2.2 \times {10^{11}}\,N/{m^2}

respectively ?

Accepted Answer

Fundamental frequency,

f = {v \over {2\ell }} = {1 \over {2\ell }}\sqrt {{T \over \mu }} = {1 \over {2\ell }}\sqrt {{T \over {A\rho }}}

\left[ {\,\,} \right.

as

v = \sqrt {{T \over \mu }}

\,\,\,\,\,\,

and

\,\,\,\,\,\,

\left. {\mu = {m \over \ell }\,\,} \right]

Also,

Y = {{T\ell } \over {A\Delta \ell }} \Rightarrow {T \over A} = {{Y\Delta \ell } \over \ell }

\Rightarrow f = {1 \over {2\ell }}\sqrt {{{\gamma \Delta \ell } \over {\ell \rho }}} ....\left( i \right)

Putting the value of

\ell ,{{\Delta \ell } \over \ell },\rho

\,\,\,\,\,\,

and

\,\,\,\,\,\,

\gamma

in

e{q^n}.\left( i \right)

we get,

f = \sqrt {{2 \over 7}} \times {{{{10}^3}} \over 3}

\,\,\,\,\,\,

or,

\,\,\,\,\,\,

f \approx 178.2\,Hz

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