For a certain organ pipe, the first three resonance frequencies are in the ratio of 1 : 3 : 5 respectively. If the frequency of fifth harmonic is 405 Hz and the speed of sound in air is 324 m s – 1 th

Question

For a certain organ pipe, the first three resonance frequencies are in the ratio of 1 : 3 : 5 respectively. If the frequency of fifth harmonic is 405 Hz and the speed of sound in air is 324 m s – 1 the length of the organ pipe is _____ m .

TestHub · Accepted Answer

It is given, f 5 = 405 Hz . As the first three resonance frequencies are in the ratio of 1 : 3 : 5 , therefore it must be a closed organ pipe. The frequency formula in a closed organ pipe is given by f = n v 4 l . So, 5 v 4 I = 405 Hz ⇒ I = 405 × 4 5 × 324 = 1 m

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