show that in the case of closed organ pipe, the ratio of the frequencies of the harmonics is 1:3:5:7.
Asked by ks076345 | 22nd Mar, 2021, 09:20: AM
Modes of vibrations to create sound wave in a tube of one closed end and other end open are shown in above figure
Wavelength λ is related to length of tube as follows
where n = 0, 1, 2, ...... etc
If v is velocity of sound wave and f is frequency , then we have
frequency f = v / λ = (2n+1) × [ v / (4L) ]
If n = 0 , fundamental mode frequency fo = [ v / (4L) ]
If n =1, first harmonic frequency f1 = 3 × [ v / (4L) ]
if n =2 , second harmonic frequency f2 = 5 × [ v / (4L) ]
Hence ratio of frequencies of harmonics = 1 : 3 : 5 : 7 ....... etc
Answered by Thiyagarajan K | 22nd Mar, 2021, 11:15: AM
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