A 3 m long organ pipe both at both ends is driven to third harmonic standing wave . If the amplitude of pressure oscillation is 0.1% of the mean atmospheric pressure (P_(0) = 10^(5) N//m^(2)). Find the amplitude of i. particle oscillation and ii. density oscillation. Speed of soundv = 330 m//s , density of air rho_(0) = 1.0 kg//m^(3)

A 3 m long organ pipe both at both ends is driven to third harmonic st

1.	A 3 m long organ pipe both at both ends is driven to third harmonic standing wave . If the amplitude of pressure oscillation is 0.1% of the mean atmospheric pressure (P_(0) = 10^(5) N//m^(2)). Find the amplitude of i. particle oscillation and ii. density oscillation. Speed of soundv = 330 m//s , density of air rho_(0) = 1.0 kg//m^(3)
Answer» <P> Solution :` 3 = 3(LAMBDA)/(2)` `lambda = 2 m` `P_(m) = 100 N//m^(2) , V = 330 m//s , rho_(0) = 1 kg//m^(3)` i. `P_(m) = Bs_(0) k = rho_(0) v^(2) s_(0) ( 2pi)/( lambda)` `s_(0)= (lambda P_(m))/( rho_(0) v^(2) 2 pi) = ( 2 xx 100)/( 1 xx 330 xx 330 xx 2 pi)` ii.`B = -( dp)/( dV//V) = (dp)/( d rho//rho)` `[ m = rho v rArr 0 = (d rho)/(rho)+ ( d v)/( v)]` `rArr d rho = (rho d p)/(B)` `( d rho)_(max) = ( rho p_(m))/( rho v ^(2)) = (100)/(108900) kg//m^(3) = (1)/( 1089) kg//m^(3)`