Question

$n_1$ is frequency of the pipe closed at one end and $N_2$ is the frequency of the pipe open open at both ends. If both are joined end to end, find the fundamental frequency of closed pipe so formed :

• A. $\frac{n_1{n}_2}{n_2+2n_1}$
• B. $\frac{n_1{n}_2}{2n_2+n_1}$
• C. $\frac{n_2+2n_1}{n_2{n}_1}$
• D. $\frac{2n_2+n_1}{n_2{n}_1}$

Answer 1

Answer: (A)

$\frac{n_1{n}_2}{n_2+2n_1}$

Frequency of a pipe closed at one end$=\frac{v}{4l_1}=n_1$

Frequency of pipe closed at both ends=$\frac{v}{2l_2}=n_2$

Joining the pipes end to end form a pipe closed at one end of length $l_1+l_2$

Thus the fundamental frequency of the closed pipe is $\frac{v}{4(l_1+l_2)}$

$=\frac{v}{4(\frac{v}{4n_1}+\frac{v}{2n_2})}$

$=\frac{n_1{n}_2}{n_2+2n_1}$