Question

A pipe closed at one end and open at the other end resonates with a sound of frequency $135Hz$ and also with $165Hz$, but not at any other frequency intermediate between these two. Then, the frequency of the fundamental note of the pipe is:

• A. $60Hz$
• B. $7.5Hz$
• C. $30Hz$
• D. $15Hz$

Answer 1

The correct option is D $15Hz$

Frequency of pipe closed at one end is given as: $\frac{(2n+1)v}{4l}$

Here, $\frac{165}{135}=\frac{2n_2+1}{2n_1+1}$ --------- {1}

and $n_2=n_1+1$
Hence, by substituting above equation in {1} and solving we get, $n_1=4$.

Thus, $n_2=5$

Thus, $165=\frac{(2n_2+1)v}{2l}$

Thus, fundamental frequency = $\frac{v}{2l}=15Hz$