Question 193: Waves

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 $$	imes$$ 103 kg/m3 and its Young’s modulus is 9.27 $$	imes$$ 1010 Pa. What will be the fundamental frequency of the longitudinal vibrations ?

Accepted Answer

As   rod length = 60 cm
$$	herefore\,\,\,$$ $${\lambda  \over 2}$$ = 60
$$ \Rightarrow $$$$\,\,\,$$ $$\lambda $$ = 120 cm = 1.2 m
In solid, velocity of wave,
V = $$\sqrt {{Y \over ho }} $$
= $$\sqrt {{{9.27 	imes {{10}^{10}}} \over {2.7 	imes {{10}^3}}}} $$
= 5.85 $$ 	imes $$ 10
3
m/sec.
As  we know,
v = f $$\lambda $$
$$	herefore\,\,\,$$ f = $${v \over \lambda }$$
= $${{5.85 	imes {{10}^3}} \over {1.2}}$$
= 4.88 $$ 	imes $$ 10
3
Hz
$$ \simeq $$  5 kHz

Answer

7.5 kHz

Answer

5 kHz

Answer

2.5 kHz

Answer

10 kHz

Waves

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 $\times 103 kg/m3 and its Young’s modulus is 9.27 \times$ 1010 Pa. What will be the fundamental frequency of the longitudinal vibrations ?

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