Q.

Figure shows a closed pipe (closed at both ends) of length 10 m. MN is a membrane (thin sheet) capable of doing simple harmonic motion of amplitude 1 mm along left and right from shown situation. On two sides of membrane are two gases  G1  and  G2  in which sound can travel at 300 m/s and 100 m/s respectively. Mark the INCORRECT statement(s). [For options C, D take maximum amplitude of standing wave patterns to be 1 mm]

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a

If resonance is obtained in right side (G2), side (G1)  might not resonate.

b

For angular frequency  75πrad/s, a particle   right of AA’ would be oscillating with maximum displacement 0.5 mm.

c

For angular frequency 75πrad/s,   a particle  23m   right of AA’ would be oscillating with maximum displacement 32mm .

d

Resonance in both gases will be possible for some specific frequencies only.

answer is D.

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Detailed Solution

V1=300m/sV2=100m/sf1=f2

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λ1:λ2=V1:V2=3:1ω=75πrad/secV=300m/sλ=8mA=Axsinkx=1sin2π8×23=0.5mm

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Figure shows a closed pipe (closed at both ends) of length 10 m. MN is a membrane (thin sheet) capable of doing simple harmonic motion of amplitude 1 mm along left and right from shown situation. On two sides of membrane are two gases  G1  and  G2  in which sound can travel at 300 m/s and 100 m/s respectively. Mark the INCORRECT statement(s). [For options C, D take maximum amplitude of standing wave patterns to be 1 mm]