Tag: melde's experiment

Questions Related to melde's experiment

The fundamental frequency of sonometer wire is 600Hz. When length wire is shorted by 25%, the frequency of ${ 1 }^{ st }$ overtone will be

physics free, damped and forced oscillations melde's experiment free, forced and damped oscillations sonometer and laws of transverse vibrations

  1. 800 Hz

  2. 1200 HZ

  3. 1600 Hz

  4. 2000 Hz

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Correct Option: C

In Melde's experiment when longitudinal position is used 4 loops are formed on string under tension of 16 g-wt . Now the string is replaced by another string of same material but of diameter half of the previous diameter and length half that of the original strings . What should be the tension in the string to obtain 2 loops on the strings , when B position is used ? 

physics free, damped and forced oscillations melde's experiment free, forced and damped oscillations sonometer and laws of transverse vibrations

  1. 16 g-wt

  2. 32 g-wt

  3. 8 g-wt

  4. 4 g-wt

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Correct Option: B

A string of length $36cm$ was in unison with a fork of frequency $256Hz$. It was in unison with another fork when the vibrating length was $48cm$, the tension being unaltered. The frequency of second fork is   

physics free, damped and forced oscillations melde's experiment free, forced and damped oscillations sonometer and laws of transverse vibrations

  1. $212Hz$

  2. $320Hz$

  3. $384Hz$

  4. $192Hz$

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Correct Option: D
Explanation:

$f=\dfrac{v }{2L}$
$v =f(2\ L)$
$=256\times 2\times 36$
$=18432\ cm/s.$


wave velocty remains same
$f=\dfrac{v }{2L}$
$=\dfrac{18432}{2\times 48}$
$=192\ Hz.$

The total mass of a wire remains constant on stretching the length of wire to four times. It's frequency will become:

physics free, damped and forced oscillations melde's experiment free, forced and damped oscillations sonometer and laws of transverse vibrations

  1. 4 times

  2. 1/2 times

  3. 8 times

  4. $\sqrt{2}$ times

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Correct Option: B
Explanation:

Frequency, $f=\dfrac{1}{2l}\sqrt{\dfrac{t}{\mu }}$


Length is made four times, but mass is same.

$\Rightarrow$ Mass per unit length is $\mu'=\dfrac{\mu }{4}$

$\Rightarrow f'=\dfrac{1}{2(4l)}\sqrt{\dfrac{t}{\frac{\mu }{4}}}$$=\dfrac{2}{2(4l)}\sqrt{\dfrac{t}{\mu }}$ 

$\Rightarrow \dfrac{f'}{f}=\dfrac{1}{2}$

$\Rightarrow f'=\dfrac{f}{2}$

The length and diameter of a metal wire is doubled. The fundamental frequency of vibration will change from '$n$' to (Tension being kept constant and material of both the wires is same)

physics free, damped and forced oscillations melde's experiment free, forced and damped oscillations sonometer and laws of transverse vibrations

  1. $\dfrac { n }{ 4 } $

  2. $\dfrac { n }{ 8 } $

  3. $\dfrac { n }{ 12 } $

  4. $\dfrac { n }{ 16 } $

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Correct Option: A
Explanation:

Fundamental frequency of vibration $n = \dfrac{v}{2L} \sqrt{\dfrac{T}{\mu}}$ 

where $\mu$ is the mass per unit length of the wire i.e. $\mu = \dfrac{M}{L}$
Mass of the wire $M = \rho (\dfrac{4\pi}{3} R^3)$
$\implies$ $n = \dfrac{v}{2L} .\sqrt{\dfrac{TL}{\rho \dfrac{4\pi }{3} R^3}}$
$\implies$ $n \propto \dfrac{1}{R\sqrt{LR}}$      .....(1)
Given :  $L _2 = 2L$  $R _2 = 2R$
From equation (1), we get  $\dfrac{n _2}{n} = \dfrac{R \sqrt{RL}}{R _2 \sqrt{L _2 R _2}}$
Or  $\dfrac{n _2}{n} = \dfrac{R \sqrt{R L}}{(2R) \sqrt{(2L) (2R)}}   = \dfrac{1}{4}$
$\implies$  $n _2 = \dfrac{n}{4}$