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  • n1 is the frequency of the pipe closed at one end and n2 is frequency of the pipe at both ends. If both are joined end to end, find the fundamental frequency of closed pipe, s

n1 is the frequency of the pipe closed at one end and n2 is frequency of the pipe at both ends. If both are joined end to end, find the fundamental frequency of closed pipe, so formed-

Option: 1

\frac{n_1 n_2}{n_2+2 n_1}


Option: 2

\frac{n_1 n_2}{2 n_2+n_1}


Option: 3

\frac{n_1+2 n_2}{n_2 n_1}


Option: 4

\frac{2 n_1+n_2}{n_2 n_1}


Answers (1)

best_answer

Frequency of closed pipe,n_1=\frac{V}{4 l_1} \Rightarrow l_1=\frac{V}{4 n_1}

Frequency for open pipe, n_2=\frac{V}{2 l_2} \Rightarrow l_2=\frac{V}{4 n_2}

Now, when both pipes are joined, then length of closed pipe-

\begin{aligned} l & =l_1+l_2 \\ \frac{V}{4 n} & =\frac{V}{4 n_1}+\frac{V}{2 n_2} \\ \frac{1}{2 n} & =\frac{1}{2 n_1}+\frac{1}{n_2} \\ \frac{1}{2 n} & =\frac{n_2+2 n_1}{2 n_1 n_n} \\ n & =\frac{n_1 n_2}{n_2+2 n_1} \end{aligned}

Posted by

sudhir.kumar

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