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 x 10³ kg/m³and its Young’s modulus is 9.27 x 10¹⁰ Pa. What will be the fundamental frequency of the longitudinal vibrations?

7.5 kHz

5 kHz

2.5 kHz

10 kHz

Solution

5 kHz

In solids, Velocity of wave

V = $\sqrt{\frac{Y}{ρ}} = \sqrt{\frac{9.27 x 10^{10}}{2.7 x 10^{3}}} v = 5.83 x 10^{3} m / s e c$

Since rod is clamped at middle fundamental wave shape is as follow

$\frac{λ}{2} = L \Rightarrow λ = 2 L λ = 1.2 m (∵ L - 60 c m = 0.6 m) u \sin g v = f λ \Rightarrow f = \frac{v}{λ} = \frac{5.85 x 10^{3}}{1.2} = 4.88 x 10^{3} H z ≅ 5 K H z$

For Daily Free Study Material Join wiredfaculty

Mechanical Properties Of Solids

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 x 10³ kg/m³and its Young’s modulus is 9.27 x 10¹⁰ Pa. What will be the fundamental frequency of the longitudinal vibrations?

7.5 kHz

5 kHz

2.5 kHz

10 kHz

Some More Questions From Mechanical Properties of Solids Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction

For Daily Free Study Material Join wiredfaculty

Mechanical Properties Of Solids

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 x 103 kg/m3 and its Young’s modulus is 9.27 x 1010 Pa. What will be the fundamental frequency of the longitudinal vibrations? 7.5 kHz 5 kHz 2.5 kHz 10 kHz

Some More Questions From Mechanical Properties of Solids Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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 x 10³ kg/m³and its Young’s modulus is 9.27 x 10¹⁰ Pa. What will be the fundamental frequency of the longitudinal vibrations?

7.5 kHz

5 kHz

2.5 kHz

10 kHz