InterviewSolution
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InterviewSolution
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A `3 m` long organ pipe open at both ends is driven to third harmonic standing wave. If the amplitude of pressure oscillations is `1` per cent of mean atmospheric pressure `(p_(o) = 10^(5) Nm^(2))`. Find the amplitude of particle displacement and density oscillations. Speed of sound `upsilon = 332 m//s` and density of air `rho = 1.03 kg//m^(3)`. |
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Answer» Correct Answer - (i) `(1)/(1089pi)m` , (ii) `(1)/(1089)kg//m^(3)` Given length of pipe `= 3m` Third harmonic Implies that `(3lambda)/(2) , lambda = (2l)/(3), = (2 xx 3)/(3) = 2 m` `k = (2pi)/(lambda) = pi` `BkS = P` `BpiS = 100` `B = rhoV^(2) = 330^(2) xx 1` `S = (100)/(piB)` `S = (100)/(pi330^(2))` `S = (1)/(1089pi)` Bulk moduls of elasticity `B = (-dp)/((dv//v))`, Volume `= (mass)/(density) = (m)/(rho)` `dv = (-m)/(rho^(2)) drho = (-Vdrho)/(rho) rArr (dv)/(V) = - (drho)/(rho) , dP = B(drho)/(rho)` `Deltarho_(max) = (rho)/(B)DeltaP_(max) = (DeltaP_(max))/(v^(2)) = (10^(2))/((330)^(2)) , (1)/(1089) kg//m^(3)` |
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