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Question

In Kundt's tube experiment, a metal rod of length 2 m and density 8 g/cm3 clamped at middle gives dust heaps in a Kundt's tube at intervals of 10 cm. Calculate the Young's modulus of the material of rod. The speed of sound, in the gas is 360 m/s.


A
2.12×1011 N/m2
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B
2.12×1010 N/m2
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C
4.14×1011 N/m2
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D
4.14×1010 N/m2
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Solution

The correct option is C 4.14×1011 N/m2
Let λr be the wavelength of sound wave in rod and λg be the wavelength of sound wave in gas tube.

Here
λr=2lr and λg=2Δlg
From Kundt's method

Let velocity of sound in gas be vg and in rod be vr

vg=Δlglrvr .......(1)
Given that
Δlg=10 cm=10×102 m
lr=2 m
Velocity of speed of sound in gas (vg)=360 m/s
Density (ρ)=8 g/cm2=8000 kg/m3
vr=Yρ=Y8000
where Y is Young's modulus.
Now substituting the value in equation (1)
360=10×1022×Y8000
Y=(360×2101)2×8000=4.14×1011 N/m2

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