If $n _{1}, n_{2}$ and $n _{3}$ are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency $n$ of the string is given by
AIPMT 2012,AIPMT 2014, Medium
Download our app for free and get started
Let $l$ be the length of the string.
Fundamental frequency is given by
$n=\frac{1}{2 l} \sqrt{\frac{T}{\mu}}$
$n \propto \frac{1}{l}(\because T \text { and } \mu \text { are constants })$
Here, $l_{1}=\frac{k}{n_{1}}, l_{2}=\frac{k}{n_{2}}, l_{3}=\frac{k}{n_{3}}$ and $l=\frac{k}{n}$
But $l=l_{1}+l_{2}+l_{3}$
$\therefore \quad \frac{1}{n}=\frac{1}{n_{1}}+\frac{1}{n_{2}}+\frac{1}{n_{3}}$
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
- 1View SolutionFrequency range of the audible sounds is
- 2If $T$ is the reverberation time of an auditorium of volume $V$ thenView Solution
- 3Transverse waves of same frequency are generated in two steel wires $A$ and $B$. The diameter of $A$ is twice of $B$ and the tension in $A$ is half that in $B$. The ratio of velocities of wave in $A$ and $B$ isView Solution
- 4A student performed the experiment to measure the speed of sound in air using resonance air-column method. Two resonances in the air-column were obtained by lowering the water level. The resonance with the shorter air-column is the first resonance and that with the longer air-column is the second resonance. Then,View Solution
$(A)$ the intensity of the sound heard at the first resonance was more than that at the second resonance
$(B)$ the prongs of the tuning fork were kept in a horizontal plane above the resonance tube
$(C)$ the amplitude of vibration of the ends of the prongs is typically around $1 \mathrm{~cm}$
$(D)$ the length of the air-column at the first resonance was somewhat shorter than $1 / 4$ th of the wavelength of the sound in air
- 5The equation for spherical progressive wave is (where $r$ is the distance from the source)View Solution
- 6A plane sound waves passes from medium $1$ into medium $2$. The speed of sound in medium $1$ is $200\,m/s$ and in medium $2$ is $100 \,m/s$. The ratio of amplitude of the transmitted wave to that of incident wave is :-View Solution
- 7View SolutionWhen a longitudinal wave propagates through a medium, the particles of the medium execute simple harmonic oscillations about their mean positions. These oscillations of a particle are characterised by an invariant
- 8A speeding motorcyclist sees traffic jam ahead him. He slows down to $36\,\, km\,\,hour^{-1}$ He finds that traffic has eased and a car moving ahead of him at $18 \,\, km\,\,hour^{-1}$ is honking at a frequency of $1392\,\, Hz.$ If the speed of sound is $343\, m s^{-1}$, the frequency of the honk as heard by him will be .... $Hz$View Solution
- 9The equation of travelling wave is $y=a \sin 2 \pi\left(p t-\frac{x}{5}\right)$. Then the ratio of maximum particle velocity to wave velocity is ...........View Solution
- 10A tuning fork vibrating with a sonometer having a wire of length $20 \,cm$ produces $5$ beats per second. The beats frequency does not change if the length of the wire is changed to $21 \,cm$. The frequency of the tuning fork must be ............ $Hz$View Solution