Question 41 of 142

A granite rod of $60cm$ length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is $2.7\times {10}^{3}kg{m}^{-3}$ and its Young's modulus is $9.27\times {10}^{10}Pa$. What will be the fundamental frequency of the longitudinal vibrations?

A$7.5kHz$B$5kHz$C$2.5kHz$D$10kHz$

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Answer: (B) $5kHz$

$L=\dfrac{⋋}{2}\Rightarrow ⋋=2L=1.2m$

$v=\sqrt{\dfrac{y}{\rho }}=5.86\times {10}^{3}m{s}^{-1}$

$∴Fundamentalfrequency=\dfrac{v}{⋋}=4.88kHz$

$\approx 5kHz$