General formula for wavelength λ=2L/n where n = 1,2,3 .........
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(1) First normal mode of vibration : n1 = v/λ1 = v/2L
This is known as fundamental frequency and the note so given is named fundamental note or first harmonic.
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(2) Second normal mode of vibration :
n2 = v/λ2 = v/L = 2n1
This is named second harmonic or first overtone.
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(3) Third normal mode of vibration : n3 = v/λ3 = 3v/2L = 3n1
This is named third harmonic or second overtone.
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Important points
(i) Comparison of open and close organ pipes defines that fundamental note in open organ pipe has double the frequency of the fundamental note in closed organ pipe
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Further in an open organ pipe all harmonics are given whereas in a closed organ pipe, only basic harmonics of frequencies etc are shown. The harmonics of frequencies 2n1, 4n1, 6n1 ...... are missing.
Hence musical sound given by an open organ pipe is sweeter than that produced by a closed organ pipe.
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(ii) Harmonics are the notes/sounds of frequency same to or an integral multiple of fundamental frequency (n). Thus the first, second, third, harmonics have frequencies ,n,2n,3n .........
(iii) Overtones are the notes/sounds of frequency twice/thrice/ four times the fundamental frequency (n) eg. 2n,3n,4n..... and so on.
(iv) In organ pipe an antinode is not created exactly at the open end rather it is created a little distance away from the open end outside it. The distance of antinode from the open end of the pipe is called as end correction.
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