Question

An open organ pipe resonated with frequency $f_1$ and 2nd harmonic. Now, one is closed and the frequency is slowly increased, then it resonates with frequency $f_2$ and the $n$th harmonic then,

• A. $n=3,f_2=\frac{1}{4}{f}_1$
• B. $n=5,f_2=\frac{3}{4}{f}_1$
• C. $n=3,f_2=\frac{5}{4}{f}_1$
• D. $n=5,f_2=\frac{5}{4}{f}_1$

Answer 1

The correct option is D $n=5,f_2=\frac{5}{4}{f}_1$

$f_1=\frac{1}{l}\sqrt{\frac{B}{\rho }}$
$f_2=\frac{n}{4l}\sqrt{\frac{B}{\rho }}\Rightarrow \frac{f_1}{f_2}=\frac{4}{n}\Rightarrow f_2=\frac{n}{4}{f}_1$