A closed organ pipe and an open organ pipe of same length produce 2 beats when they are set into vibrations…
A closed organ pipe and an open organ pipe of same length produce 2 beats when they are set into vibrations simultaneously in their fundamental mode. The length of open organ pipe is now halved and of closed organ pipe is doubled. The number of beats produced will be
8
7
4
2
Solution
We have, $f - \frac{f}{2} = 2 \Rightarrow f = 4\text{ Hz}$
Here, $f = \frac{v}{2l} =\text{ fundamental frequency of open pipe}$
and $\frac{f}{2} = \frac{v}{4l} =\text{ fundamental frequency of closed pipe}$
Now, new beat frequency
$= 2f - \frac{f}{4} = \frac{7f}{4} = \frac{7}{4} \times 4 = 7\text{ Hz}$