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

Correct Answer: 740

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 \( v = 333 \, \text{m/s} \):
\[\Delta f = \frac{6 \times 333}{2 \times 0.6} - \frac{5 \times 333}{2 \times 0.9}\]
\[\Delta f = 740 \, \text{Hz}\]