Question

A cylindrical metal tube has a length of 50 cm and is , open at both ends. Find the frequencies between 1000 Hz and 2000 Hz at which the air column in the tube can resonate. Speed of sound in air is $340m{s}^{-1}$.

Answer 1

Here given that,

I =50 cm, v=340 m/s

As it is an open organ pipe the fundamental frequency,

$f_1=\left(\frac{v}{2I}\right)$

$=\frac{340}{2\times 50\times {10}^{-2}}=340$ Hertz

So the harmonics are,

$f_3=3\times 340=1020Hz$

$f_5=5\times 340=1700Hz$

$f_6=6\times 340=2040Hz$

So the possible frequecies are between 1000 Hz and 2000 Hz are 1020,1360,1700.