Question

An open pipe is suddenly closed at one end as a result of which the frequency of the third harmonic of the closed pipe is found to be higher by $100Hz$ than the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is

• A. $200Hz$
• B. $300Hz$
• C. $240Hz$
• D. $480Hz$

Answer 1

The correct option is A $200Hz$

For an organ pipe open at both ends

$f_n=\frac{nv}{2L}$ .....(1) where f stands for for pipe open at both ends

For an organ pipe closed at one end

$f_n^{\prime }=\frac{(2n-1)v}{4L}$ .....(2) where f' stands for for pipe closed at one end

From eqn(1)

$f_3=\frac{2v}{2L}$

From (2)

$f_3^{\prime }=\frac{5v}{4L}$

Given, $f_3^{\prime }-f_3=100$

$\therefore \frac{v}{4L}=100$

$\Rightarrow f_1=\frac{v}{2L}=2\times \frac{v}{4L}=2\times 100=200Hz$