Question

An open pipe resonates to a frequency f${}_1$ and a 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 corrections)

• A. $\frac{f_1{f}_2}{2f_2+f_1}$
• B. $\frac{f_1{f}_2}{f_2+2f_1}$
• C. $\frac{2f_1{f}_2}{f_2+f_1}$
• D. $\frac{f_1+2f_2}{f_1{f}_2}$

Answer 1

The correct option is A $\frac{f_1{f}_2}{2f_2+f_1}$

Joining an open pipe and a closed pipe will make a closed pipe combination.

Resonance frequency for an open pipe, $f_1=\frac{v}{2L_o}$

Resonance frequency for closed pipe, $f_2=\frac{v}{4L_c}$

Resonance frequency of combined closed pipe $f=\frac{v}{4(L_o+L_c)}$

=> $f=\frac{v^2}{8L_o{L}_c}\times \frac{2L_o{L}_c}{v(L_o+L_c)}$

=> $f=\frac{f_1{f}_2}{2f_2+f_1}$