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  4. A cylindrical tube closed at one end contains air. It produces the fundamental note of frequency 512 Hz. If the tube is opened at both ends, the fundamental frequency that can be excited is

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Q. A cylindrical tube closed at one end contains air. It produces the fundamental note of frequency $512\, Hz$. If the tube is opened at both ends, the fundamental frequency that can be excited is

ManipalManipal 2010Electromagnetic Waves

Solution:

Let $l$ be the length of pipe, $v$ the speed of sound, then the fundamental tone or first harmonic of closed tube
image
$n_{1}=\frac{v}{4 l}$
For open tube
$n_{2}=\frac{v}{2 l} $
$\therefore n_{2}=2 n_{1} $
Given, $ n_{1}=512 \,Hz $
$\therefore n_{2}=2 \times 512=1024 \,Hz$