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  4. A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is 2.7 × 103 kg/m3 and its Young's modules is 9.27 × 1010 Pa. What will be the fundamental frequency of the longitudinal vibrations ?

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Q. A granite rod of $60\, cm$ 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 modules is $9.27 \times 10^{10}\, Pa$. What will be the fundamental frequency of the longitudinal vibrations ?

JEE MainJEE Main 2018Waves

Solution:

$f_{0}=\frac{V}{2 L}=\frac{1}{2 L} \sqrt{\frac{Y}{\rho}}$
$=\frac{1}{2 \times 0.6} \sqrt{\frac{9.27 \times 10^{10}}{2.7 \times 10^{3}}} $
$=4.88 \,kHz \approx 5\, kHz$