A granite rod of 60cm length is clamped at its middle point and is...

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 granite rod of 60cm length is clamped at its middle point and is set into longitudinal vibrations. The density of

A granite rod of 60cm length is clamped at its middle point and is set into longitudinal vibrations. The density of

Options

A $7 . 5kHz$
B $5kHz$
C $2 . 5kHz$
D $10kHz$

Correct answer

B. $5kHz$

Step-by-step solution

L = \dfrac{⋋}{2} ⇒ ⋋ = 2L = 1.2m

v = \sqrt{\dfrac{y}{ρ}} = 5.86 \times {10}^{3}m{s}^{- 1}

∴ Fundamental frequency = \dfrac{v}{⋋} = 4.88kHz

\approx 5kHz

Practice Waves and Sound on Quantrex Academy →

More from Waves and Sound

List-I shows four configurations made of straight and semi-circular narrow tubes… JEE Advanced 2026 A transverse wave on a string is described by y = 3 (36t + 0.018x + π/4) , where x, y are… JEE Main 2026 The equation of a plane progressive wave is given by y = 5 π(200t - (x)/(150)) where x… JEE Main 2026 The speed of a longitudinal wave in a metallic bar is 400 ~m / s . If the density and… JEE Main 2026 Two tuning forks A and B are sounded together giving rise to 8 beats in 2 s. When fork A… JEE Main 2026 A point source is kept at the center of a spherically enclosed detector. If the volume of… JEE Main 2026 The fifth harmonic of a closed organ pipe is found to be in unison with the first… JEE Main 2026 The velocity of sound in air is doubled when the temperature is raised from 0^ ∘ C to α^… JEE Main 2026 Full Waves and Sound list All JEE Main PYQs