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 modulus is $9.27 \times 10^{10}$ $Pa$ What will be the fundamental frequency of the longitudinal vibrations .... $kHz$ ?
JEE MAIN 2018, Diffcult
Download our app for free and get started
In solids, Velocity of wave $V=\sqrt{\frac{Y}{\rho}}=\sqrt{\frac{9.27 \times 10^{10}}{2.7 \times 10^{3}}}$
$\mathrm{v}=5.85 \times 10^{3} \mathrm{m} / \mathrm{sec}$
since rod is clamped at middle fundamental wave shape is as follow
$\frac{\lambda}{2}=\mathrm{L} \Rightarrow \lambda=2 \mathrm{L}$
$\lambda=1.2 \mathrm{m}(\because \mathrm{L}=60 \mathrm{cm}=0.6 \mathrm{m}(\mathrm{given})$
Using $v=f \lambda$
$\Rightarrow \quad f=\frac{v}{\lambda}=\frac{5.85 \times 10^{3}}{1.2}$
$=4.88 \times 10^{3} \mathrm{Hz}=5 \mathrm{KHz}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A wave represented by the equation ${y_1} = a\,\cos \,\left( {kx - \omega t} \right)$ is superimposed with another wave to form a stationary wave such that the point $x = 0$ is node. The equation for the other wave isView Solution
- 2A tuning fork and a sonometer wire were sounded together and produce $4$ beats per second. When the length of sonometer wire is $95 cm$ or $100 cm,$ the frequency of the tuning fork is ..... $Hz$View Solution
- 3A group of people watch a ice show which is held in closed area . Skaters perform a . music show whose level is $60\ db$ . Spectator can yell at $40.0 \ dB$ . Which one of the them represent approx combine sound levelView Solution
- 4There are three sources of sound of equal intensity with frequencies $400, 401$ and $402\, vib/sec.$ The number of beats heard per second isView Solution
- 5A steel wire with mass per unit length $7.0 \times 10^{-3}\,kg\,m ^{-1}$ is under tension of $70\,N$. The speed of transverse waves in the wire will be $.........m/s$View Solution
- 6A closed organ pipe has a frequency $'n'$. If its length is doubled and radius is halved, its frequency nearly becomes-View Solution
- 7A closed organ pipe of length $l$ is sounded together with another closed organ pipe of length $l + x (x << l)$ both in fundamental mode. If $v$ = speed of sound, the beat frequency heard isView Solution
- 8An organ pipe of length $L$ open at both ends is found to vibrate in its first harmonic when sounded with a tuning fork of $480\, Hz$. What should be the length of a pipe closed at one end, so that it also vibrates in its first harmonic with the same tuning fork ?View Solution
- 9View SolutionThe phenomenon of sound propagation in air is
- 10In resonance tube two successive positions of resonance are obtained at $15 \,cm$ and $48 \,cm$. If the frequency of the fork is $500 \,cps$, the velocity of sound is ......... $m / s$View Solution