Question

Two open organ pipes of length $60 \, \text{cm}$ and $90 \, \text{cm}$ resonate at $6^\text{th}$ and $5^\text{th}$ harmonics respectively. The difference of frequencies for the given modes is ____ $\text{Hz}$.
(Velocity of sound in air $= 333 \, \text{m/s}$)

Answer 1

The frequency $f$ of an open organ pipe is given by:
$f = \frac{nv}{2L}$
The difference in frequency $\Delta f$ for the two pipes is:
$\Delta f = \frac{6v}{2 \times 0.6} - \frac{5v}{2 \times 0.9}$
Substitute $v = 333 \, \text{m/s}$:
$\Delta f = \frac{6 \times 333}{2 \times 0.6} - \frac{5 \times 333}{2 \times 0.9}$
$\Delta f = 740 \, \text{Hz}$