Fundamental frequency of sonometer wire is $n$. If the length, tension and diameter of wire are tripled, the new fundamental frequency is
Medium
Download our app for free and get started
(d) $n = \frac{1}{{2l}}\sqrt {\frac{T}{{\pi {r^2}\rho }}}$
$\Rightarrow n \propto \frac{{\sqrt T }}{{lr}}$
==> $\frac{{{n_1}}}{{{n_2}}} = \sqrt {\frac{{{T_1}}}{{{T_2}}}} \times \frac{{{l_2}}}{{{l_1}}} \times \frac{{{r_2}}}{{{r_1}}}$
$ = \sqrt {\frac{T}{{3T}}} \times \frac{{3l}}{l} \times \frac{{2r}}{r} = 3\sqrt 3 $
==> ${n_2} = \frac{n}{{3\sqrt 3 }}$
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
- 1The fundamental frequency of vibration of a string stretched between two rigid support is $50\,Hz$. The mass of the string is $18\,g$ and its linear mass density is $20\,g / m$. The speed of the transverse waves so produced in the string is $..........\,ms ^{-1}$View Solution
- 2View SolutionStanding stationary waves can be obtained in an air column even if the interfering waves are
- 3A sonometer wire, with a suspended mass of $M = 1\, kg$, is in resonance with a given tuning fork. The apparatus is taken to the moon where the acceleration due to gravity is $(1/6)$ that on earth. To obtain resonance on the moon, the value of $M$ should be ......... $kg$View Solution
- 4View SolutionBeats are the result of
- 5The speed of sound in oxygen $\left( O _{2}\right)$ at a certain temperature is $460 \;ms ^{-1}$. The speed of sound in helium $(He)$ at the same temperature will be (asume both gases to be ideal)View Solution
- 6A tuning fork of unknown frequency produoes $4$ beats per second when sounded with another tuning fork of frequency $254 \,Hz$. It gives the same number of beats per second when unknown tuning fork loaded with wax. The unknown frequency before loading with wax is ..........View Solution
- 7The driver of a car travelling with speed $30 \,\,m/s$ towards a hill sounds a horn of frequency $600\,\, Hz.$ If the velocity of sound in air is $330 \,\,m/s$, the frequency of reflected sound as heard by driver is .... $Hz$View Solution
- 8If the length of a closed organ pipe is $1m $ and velocity of sound is $330 m/s$, then the frequency for the second note isView Solution
- 9A transverse wave is represented byView Solution
$y = \frac{{10}}{\pi }\,\sin \,\left( {\frac{{2\pi }}{T}t - \frac{{2\pi }}{\lambda }x} \right)$
For what value of the wavelength the wave velocity is twice the maximum particle velocity ..... $cm$ ?
- 10Two sound sources when sounded simultaneously produce four beats in $0.25$ second. the difference in their frequencies must beView Solution