Question

An organ pipe is closed at one end and open at the other. What is the ratio of frequencies of the $3^\text{rd}$ and $4^\text{th}$ fundamental modes of vibration?

• A. $ \frac{3}{4} $
• B. $ \frac{5}{7} $
• C. $ \frac{3}{5} $
• D. $ \frac{9}{11} $

Answer 1

Answer: (B)

The frequency of $3^\text{rd}$ fundamental mode of vibration.
$v_{3}=\frac{5 v}{4 L}$
The frequency of $4^\text{th}$ fundamental mode of vibration
$v_{4}=\frac{7 v}{4 L} \frac{v_{3}}{v_{4}}=\frac{5}{7}$