Question

A cylindrical metal tube has a length of $50\text{cm}$ and is open at both ends. Find the frequencies between $1\text{kHz}$ to $2\text{kHz}$ at which the air column in the tube resonates. The temperature on that day is ${20}^{\circ }C$.
[Take $v_0=330\text{m/s}$]

• A. $1020,11360,1700\text{Hz}$
• B. $1026,1368,1710\text{Hz}$
• C. $1328,1660,1922\text{Hz}$
• D. None of these

Answer 1

The correct option is B $1026,1368,1710\text{Hz}$

As per the question we have
$f_n=\frac{nv}{2L}$
Also, $v\left(T\right)=v_0\sqrt{1+\frac{T}{273}}$
$\Rightarrow v=330\sqrt{1+\frac{20}{273}}=330\sqrt{\frac{293}{273}}=342{\text{ms}}^{-1}$
$\Rightarrow f_n=\frac{342n}{2L}=\frac{342n}{2\times 50\times {10}^{-2}}\text{Hz}$
Thus, wavelengths allowed between $1000\text{Hz}$ and $2000\text{Hz}$ are for $n=3,4,5$, so, the values are
$1026\text{Hz},1368\text{Hz},1710\text{Hz}$.