Organ pipes are the musical instruments which are used for producing musical sound by blowing air into the line. Longitudinal stationary pulses are formed on account of superimposition of incident and reflected longitudinal waves.
Equation of standing wave y = 2a cos2πvt/λ sin2πx/λ
General formula for wavelength λ = 4L/(2n-1)
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(1) First normal mode of vibration : n1 = v/4L
This is called fundamental frequency. The note so given is known as fundamental note or first harmonic.
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(2) Second normal mode of vibration : n2 = 3v/4L=3n1
This is known as third harmonic or first overtone.
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(3) Third normal mode of vibration : n3 = 5v/4L=5n1
This is known as fifth harmonic or second overtone.
Position of nodes : x = 0,2L/(2n-1), 4L/(2n-1), 6L/(2n-1)....... 2nL/(2n-1)
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For first mode of vibration x = 0 [One node]
For second mode of vibration x = 0, x =2L/3 [Two nodes]
For third mode of vibration x = 0, x =2L/5, 4L/5 [Three nodes]
Position of antinode : x =L/(2n-1), 3L/(2n-1), 5L/(2n ..........,L
For first mode of vibration x = L [One antinode]
For second mode of vibration x = L/3,x = L [Two antinode]
For third mode of vibration x = L/5,3L/5,L [Three antinode]
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