A pipe closed at one end and open at the other end resonates with a sound of frequency $135\text{ Hz}$ and…
A pipe closed at one end and open at the other end resonates with a sound of frequency $135\text{ Hz}$ and also with $165\text{ Hz}$, but not at any other frequency intermediate between these two. Then, the frequency of the fundamental note of the pipe is [EAMCET 2013]
$15\text{ Hz}$
$60\text{ Hz}$
$7.5\text{ Hz}$
$30\text{ Hz}$
Solution
The frequency of the fundamental note of the pipe is
$n_2 - n_1 = 2\left(\frac{v}{4l}\right) \Rightarrow \frac{v}{4l} = \frac{n_2 - n_1}{2}$
Given, $n_1 = 135\text{ Hz}$ and $n_2 = 165\text{ Hz}$
Now, $\frac{v}{4l} = \frac{165 - 135}{2} = \frac{30}{2} = 15\text{ Hz}$