Two vibrating strings of same material but lengths L and 2L have radii 2r and r respectively. They a

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14.Waves and Sound

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Two vibrating strings of the same material but lengths $L$ and $2L$ have radii $2r$ and $r$ respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of length $L$ with frequency $n_1$ and the other with frequency $n_2$. The ratio $n_1/n_2$ is given by

$2$

$4$

$8$

$1$

(IIT-2000)

Solution

(d) Fundamental frequency $n = \frac{1}{{2l}}\sqrt {\frac{T}{{\pi {r^2}\rho }}} $

where $m =$ Mass per unit length of wire

==>$n \propto = \frac{1}{{lr}} \Rightarrow \frac{{{n_1}}}{{{n_2}}} = \frac{{{r_2}}}{{{r_1}}} \times \frac{{{l_2}}}{{{l_1}}} = \frac{r}{{2r}} \times \frac{{2L}}{L} = \frac{1}{1}$

Standard 11

Physics

A block $\mathrm{M}$ hangs vertically at the bottom end of a uniform rope of constant mass per unit length. The top end of the rope is attached to a fixed rigid support at $O$. A transverse wave pulse (Pulse $1$ ) of wavelength $\lambda_0$ is produced at point $O$ on the rope. The pulse takes time $T_{O A}$ to reach point $A$. If the wave pulse of wavelength $\lambda_0$ is produced at point $A$ (Pulse $2$) without disturbing the position of $M$ it takes time $T_{A 0}$ to reach point $O$. Which of the following options is/are correct?

(image)

[$A$] The time $\mathrm{T}_{A 0}=\mathrm{T}_{\mathrm{OA}}$

[$B$] The velocities of the two pulses (Pulse $1$ and Pulse $2$) are the same at the midpoint of rope.

[$C$] The wavelength of Pulse $1$ becomes longer when it reaches point $A$.

[$D$] The velocity of any pulse along the rope is independent of its frequency and wavelength.

normal

(IIT-2017)

If the tension of sonometer’s wire increases four times then the fundamental frequency of the wire will increase by …. $ times$

easy

Two identical strings $X$ and $Z$ made of same material have tension $T _{ x }$ and $T _{ z }$ in them. If their fundamental frequencies are $450\, Hz$ and $300\, Hz ,$ respectively, then the ratio $T _{ x } / T _{ z }$ is$…..$

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(JEE MAIN-2020)

A tunning fork produces $5\, beats/sec$ when the length of a sonometer wire is either $1\, m$ or $1.05\, m$. Calculate the frequency of tunning fork …. $Hz$

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A light wave travels through three transparent materials of equal thickness. Rank in order, from the highest to lowest, the indices of refraction $n_1, n_2$ and $n_3$.

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Solution

Similar Questions

If the tension of sonometer’s wire increases four times then the fundamental frequency of the wire will increase by …. $ times$

Two identical strings $X$ and $Z$ made of same material have tension $T _{ x }$ and $T _{ z }$ in them. If their fundamental frequencies are $450\, Hz$ and $300\, Hz ,$ respectively, then the ratio $T _{ x } / T _{ z }$ is$…..$

A tunning fork produces $5\, beats/sec$ when the length of a sonometer wire is either $1\, m$ or $1.05\, m$. Calculate the frequency of tunning fork …. $Hz$

A light wave travels through three transparent materials of equal thickness. Rank in order, from the highest to lowest, the indices of refraction $n_1, n_2$ and $n_3$.

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