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Question

When a narrow resonance column apparatus is filled with ozone gas (γ=4/3), it resonates in 1st resonance with a tuning fork. When it is filled with nitrogen gas N2, it resonates with the same tuning fork in 1st resonance when water column is shifted down by 10 cm. Neglect end correction and take 5=2.25.

A
Wavelength of sound in ozone is approximately 1 m
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B
Wavelength of sound in nitrogen is approximately 1.6 m
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C
For second resonance in ozone gas, the water column should be shifted by 60 cm
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D
For second resonance in nitrogen gas, the water column should be shifted by 80 cm
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Solution

The correct options are
B Wavelength of sound in nitrogen is approximately 1.6 m
C For second resonance in ozone gas, the water column should be shifted by 60 cm
D For second resonance in nitrogen gas, the water column should be shifted by 80 cm
Fundamental frequency of an air column closed at one end
For ozone :
n1O3=VO34L=14LγO3RTMO3

For nitrogen :
n1N2=VN24(L+10)=14(L+10)γN2RTMN2



n103n1N2=L+10L4×5×283×7×48
L+10L=32.252.25L+22.5=3L

0.75L=22.5
L=22.50.75=30 cm

a) Wavelength of sound in O3 λ03=4L=1.2 m


b) Wavelength of sound in N2 λN2=4(L+10)= 1.6 m


c) L1= 30 cm
Length of water column for second resonance L2=3L1=90 cmL2L1=60 cm (ForO3)

d) L1=40 cm
Length of water column for second resonance L2=3L1=120 cmL2L1=80 cm(ForN2)

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