Question

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. $10kHz$
• B. $7.5kHz$
• C. $5kHz$
• D. $2.5kHz$

Answer 1

The correct option is C $5kHz$

$f_0=\frac{1}{2\ell }\sqrt{\frac{Y}{\rho }}=\frac{1}{2\left(0.6\right)}\sqrt{\frac{9.27\times {10}^{10}}{2.7\times {10}^3}}$
$=4.9\times {10}^{3}Hz\simeq 5kHz$