Question 413: Waves

Question

An open organ pipe and a closed organ pipe have the frequency of their first overtone identical. The ratio of length of open pipe to that of closed pipe is

Accepted Answer

The frequency higher than the fundamental frequency of sound is known as an overtone.
For an open organ pipe, the first overtone is given by:
$ v_o = \frac{2v}{2L_o} = \frac{v}{L_o} $
For a closed organ pipe, the first overtone is:
$ v_c = \frac{3v}{4L_c} $
It is provided that the first overtones of both pipes are identical:
$ v_o = v_c $
Substituting the expressions for the overtones, we have:
$ \frac{v}{L_o} = \frac{3v}{4L_c} $
By simplifying this equation, we find the ratio of the lengths of the open pipe to the closed pipe:
$ \frac{L_o}{L_c} = \frac{4}{3} $

Answer

$$1: 2$$

Answer

$$3: 4$$

Answer

$$4: 3$$

Answer

$$2: 1$$

Waves

An open organ pipe and a closed organ pipe have the frequency of their first overtone identical. The ratio of length of open pipe to that of closed pipe is

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