Question

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 ?

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

Answer 1

Answer: (A)

5 kHz

Answer 2

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