Question

A pipe closed at one end produces a fundamental frequency of $375\text{Hz}$. If it is cut into two pipes of equal length, then the fundamental frequency produced by the open and closed pipes respectively are

• A. $750\text{Hz},1000\text{Hz}$
• B. $750\text{Hz},750\text{Hz}$
• C. $375\text{Hz},750\text{Hz}$
• D. $1500\text{Hz},750\text{Hz}$

Answer 1

The correct option is D $1500\text{Hz},750\text{Hz}$

For the original pipe,
Fundamental frequency,
$f_o=\frac{v}{4l}$
$\Rightarrow 375=\frac{v}{4l}$
$\Rightarrow l=\frac{v}{1500}$
When it is cut into two pipes of equal length, then one pipe will be closed and the other will be open.
For open pipe,
Fundamental frequency,
$f_o=\frac{v}{2l^{{}^{\prime }}}$
$[l^{{}^{\prime }}=\frac{l}{2}]$
$\Rightarrow f_o=\frac{v}{2\times \frac{v}{2\times 1500}}=1500\text{Hz}$

For closed pipe,
Fundamental frequency,
$f_o=\frac{v}{4l^{{}^{\prime }}}$
$[l^{{}^{\prime }}=\frac{l}{2}]$
$\Rightarrow f_o=\frac{v}{4\times \frac{v}{2\times 1500}}=750\text{Hz}$