Question

An open organ pipe resonates with frequency $f_1$ and $2^{nd}$ harmonic. Now one end is closed and the frequency is slowly increased till it resonates with frequency $f_2$ and nth harmonic then

• A. $n=3,f_2=\frac{3}{4}{f}_1$
• B. $n=5,f_2=\frac{3}{4}{f}_1$
• C. $n=3,f_2=\frac{5}{4}{f}_1$
• D. $n=5,f_2=f_1\frac{5}{4}$

Answer 1

The correct option is D $n=5,f_2=f_1\frac{5}{4}$

$f_1=\frac{1}{l}\sqrt{\frac{B}{\rho }}$

$f_1=\frac{1}{4l}\sqrt{\frac{B}{\rho }}$

$\Rightarrow \frac{f_1}{f_2}=\frac{4}{n}$

$\Rightarrow f_2=\frac{n}{4}{f}_1$

For first resonance, $n=5,f_2=\frac{5}{4}{f}_1$