A wire of length $L$ and mass per unit length $6.0\times 10^{-3}\; \mathrm{kgm}^{-1}$ is put under tension of $540\; \mathrm{N}$. Two consecutive frequencies that it resonates at are : $420\; \mathrm{Hz}$ and $490 \;\mathrm{Hz}$. Then $\mathrm{L}$ in meters is
JEE MAIN 2020, Diffcult
Download our app for free and get started
$\frac{\mathrm{nv}}{2 \ell}=420$
$\frac{(\mathrm{n}+1) \mathrm{v}}{2 \ell}=490$
$\frac{v}{2 \ell}=70$
$\ell=\frac{\mathrm{v}}{140}=\frac{1}{140} \sqrt{\frac{540}{6 \times 10^{-3}}}=\frac{1}{140} \sqrt{90 \times 10^{3}}$
$\ell=\frac{300}{140}=2.142$
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
- 1An observer moves towards a stationary source of sound with a velocity equal to one-fifth of the velocity of sound. The percentage change in the frequency will be $\dots \;$%View Solution
- 2A source and an observer approach each other with same velocity $50 m/s$. If the apparent frequency is $435 \,s^{-1}$, then the real frequency is .... $s^{-1}$View Solution
- 3Two close organ pipe having length $20\,cm$ and $20.5\, cm$ produce $5\, beats/sec$. Determine the frequency of both organ pipeView Solution
- 4The frequency of transverse vibrations in a stretched string is $200 Hz$. If the tension is increased four times and the length is reduced to one-fourth the original value, the frequency of vibration will be .... $Hz$View Solution
- 5When the temperature of an ideal gas is increased by $600 K$, the velocity of sound in the gas becomes $\sqrt 3 $ times the initial velocity in it. The initial temperature of the gas is .... $^oC$View Solution
- 6Oxygen is $16$ times heavier than hydrogen. Equal volumes of hydrogen and oxygen are mixed. The ratio of speed of sound in the mixture to that in hydrogen isView Solution
- 7View SolutionQuality of a musical note depends on
- 8In a transverse wave the distance between a crest and neighbouring trough at the same instant is $4.0\, cm$ and the distance between a crest and trough at the same place is $1 .0\, cm$ . The next crest appears at the same place after a time interval of $0.4\,s$. The maximum speed of the vibrating particles in the medium isView Solution
- 9Two vehicles, each moving with speed $u$ on the same horizontal straight road, are approaching each other. Wind blows along the road with velocity $w$. One of these vehicles blows a whistle of frequency $f_1$. An observer in the other vehicle hears the frequency of the whistle to be $f _2$. The speed of sound in still air is $V$. The correct statement$(s)$ is (are) :View Solution
$(A)$ If the wind blows from the observer to the source, $f_2 > f_1$.
$(B)$ If the wind blows from the source to the observer, $f_2 > f_1$.
$(C)$ If the wind blows from the observer to the source, $f _2 < f _1$.
$(D)$ If the wind blows from the source to the observer, $f _2 < f _1$.
- 10It takes $2.0$ seconds for a sound wave to travel between two fixed points when the day temperature is ${10^o}C.$ If the temperature rise to ${30^o}C$ the sound wave travels between the same fixed parts in ...... $sec$View Solution