The number of possible natural oscillations of air column in a pipe closed at one end of length $85\text{…
The number of possible natural oscillations of air column in a pipe closed at one end of length $85\text{ cm}$ whose frequencies lie below $1250\text{ Hz}$ are
(Take, velocity of sound $= 340\text{ ms}^{-1}$)
4
5
7
6
Solution
For a pipe closed at one end,
$f_n = n \left(\frac{v}{4l}\right)$, here $n$ is an odd number
$= n \left(\frac{340}{4 \times 85 \times 10^{-2}}\right) = n (100)$
Here, $n$ is an odd number, so for the given condition, $n$ can go upto $n = 11$ because for $n = 13$, condition will not be valid.
$n = 1, 3, 5, 7, 9, 11$
So, number of possible natural oscillations could be 6.