Question

A cylindrical metal tube has a length of $50cm$ and is open at both ends. The frequencies between $1kHz$ to $2kHz$ at which the air column in the tube resonates are $($the temperature on that day is ${20}^{o}C(V_0=330m/s)$

• A. 1020, 11360, 1700 Hz
• B. 1026, 1368, 1710 Hz
• C. 1328, 1660, 1922 Hz
• D. 1020, 1136, 1700 Hz

Answer 1

The correct option is B 1026, 1368, 1710 Hz

For an organ pipe open at both ends:

$f_n=\frac{nv}{2L}...................\left(1\right)$

But $v$ is dependent on temp.

$v=v_0\sqrt{(1+\frac{t}{273})}=330\sqrt{(1+\frac{20}{273})}=342$

Substituting $v$ in $\left(1\right),$ we get,

$f_n=\frac{342n}{2L}=\frac{342n}{2\times 50\times {10}^{-2}}$

The values of frequencies allowed between $1kHz$ and and $2kHz$ are for $n=3,4,5$

The values are $1026,1368,1710Hz$.