Study of Vibrations of Air Columns

The fundamental frequency of an air column in a pipe closed at one end is in unison with the third overtone of an open pipe. Calculate the ratio of lengths of their air columns

In a set, 21 turning forks are arranged in a series of decreasing frequencies. Each tuning fork produces 4 beats per second with the preceding fork. If the first fork is an octave of the last fork, find the frequencies of the first and tenth fork.

A pipe open at both ends resonates to a frequency ‘n₁’ and a pipe closed at one end resonates to a frequency ‘n₂’. If they are joined to form a pipe closed at one end, then the fundamental frequency will be ______.

(A)  `(n_1n_2)/(2n_2+n_1)`

(B) `(2n_2n_1)/(2n_2+n_1)`

(C) `(2n_2n_1)/(n_1+n_2)`

(D) `(n_2+2n_1)/(n_1n_2)` 

The value of end correction for an open organ pipe of radius 'r' is .........................

A) 0.3 r

B) 0.6 r

C) 0.9 r

D) 1.2 r

Discuss different modes of vibrations in an air column of a pipe open at both the ends.

What is meant by harmonics?

State the cause of end correction.

Draw neat labelled diagrams for modes of vibration of an air column in a pipe when it is closed at one end.

Hence derive an expression for fundamental frequency in each case.