A 3 m long organ pipe open 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 sound v = 330 m/s, density of air ρ 0 = 1.0 kg/m 3 .
Text Solution
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((i) 
m (ii) 
kg/m 3 )
Given length of pipe = 3 m
Third harmonic implies that 
= λ λ = 
= 
= 2 m
k = 
= π
BkS = P
B π S = 100
B = ρ V 2 = 330 2 × 1
S = 
S = 
S = 
Bulk moduls of elasticity
B = 
Volume = 
= 
dv = 
d ρ = 
⇒ 
= – 
dP = B 
Δρ max = 
Δρ P max = 
= 
= 
kg/m 3
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