The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is

Question

The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is (A) 16 cm (B) 13.3 cm (C) 12.5 cm (D) 8 cm

Tardigrade Admin · Accepted Answer

For closed organ pipe, third harmonic = (3v/4l) For open organ pipe, fundamental frequency = (v/2l') Given, (3v/4l) = (v/2l') ⇒ l' = (4l/3 ×2) = (2l/3) = (2 ×20/3) = 13.33 cm

Q. The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is $20 c m$ , the length of the open organ pipe is

16 cm

13.3 cm

12.5 cm

8 cm

For closed organ pipe, third harmonic
$= \frac{3 v}{4 l}$
For open organ pipe, fundamental frequency
$= \frac{v}{2 l ^{'}}$
Given,
$\frac{3 v}{4 l} = \frac{v}{2 l ^{'}}$
$\Rightarrow l^{'} = \frac{4 l}{3 \times 2} = \frac{2 l}{3}$
$= \frac{2 \times 20}{3}$
$= 13.33 c m$

Q. The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is 20cm, the length of the open organ pipe is