Question

A pipe opened at both ends produces a note of frequency $f_1.$ When the pipe is kept with $\frac{3}{4}$th of its ength in water, it produces a note of frequency $f_2.$ The ratio $\frac{f_1}{f_2}$ is

• A. $\frac{3}{4}$
• B. $\frac{4}{3}$
• C. $\frac{1}{2}$
• D. 2

Answer 1

Answer: (C)

For open pipe $f_1 = \frac{v}{2l}$ and for closed pipe
$ f_2 = \frac{v}{4 \times\big(\frac{l}{4}\big)}=\frac{v}{l} = 2f_1$
$\Rightarrow \frac{f_1}{f_2}=\frac{1}{2} $