Question

An open pipe resonates to a frequency $'f_{1}'$ and closed pipe resonates to a frequency $'f_{2}'.$ If they are joined together to form a longer tube. Then it will resonate to a frequency of (Neglect end correction

• A. $\frac{2 f_{1} f_{2}}{2 f_{2} + f_{1}}$
• B. $\frac{f_{1} f_{2}}{f_{2} + 2 f_{1}}$
• C. $\frac{2 f_{1} f_{2}}{f_{1} + f_{2}}$
• D. $\frac{f_{1} f_{2}}{f_{1} + 2 f_{2}}$

Answer 1

Answer: (D)

$f_{1}=\frac{V}{2 \ell _{1}}$ $\ell _{1}=\frac{V}{2 f_{1}},\ell _{2}=\frac{V}{4 f_{2}}$
$f=\frac{V}{4 \ell }$ $f=\frac{V}{4 \left[\frac{V}{2 f_{1}} + \frac{V}{4 f_{2}}\right]}$ $\boxed{f = \frac{f_{1} f_{2}}{f_{1} + 2 f_{2}}}$