Question

An open and closed organ pipe have same length . The ratio of frequency of their nth overtone is ?

Answer 1

Answer:

2(n+1)/2n+1

Explanation:

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Answer 2

Answer:

The ratio of frequency of their nth overtone is (2n-1)/2n.

Explanation:

concept:

• A open pipe is the organ pipe in which both ends are open. So nodes antinodes are produced at the open end. The closed pipe in which both  sides are closed and nodes produced at both ends.
• An overtone is any harmonic with frequency greater than the fundamental frequency of a sound.
• Formula to find the possible frequencies in a closed pipes

                               f = (2 n - 1) v /4 L

• Where n = 0, 1, 2, 3,..., v = the speed of sound and Length L = λ/4

Description:

Consider L be the length of the pipe and v be the speed of the sound and f be the  frequency of wave.

• The frequency of the CLOSED organ pipe of 'n'th overtone

                                $f=\frac{(2n-1)v}{4L}$.........................(1)

• Frequency of OPEN organ pipe of nth overtone is,

                           $f'=\frac{nv}{2L}$.......................................(2)

The ratio = (2)/(1)

          $\frac{f'}{f} = \frac{2n-1}{2n}$

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