An organ pipe is closed at one end and open at the other. What is the ratio of frequencies of the 3 textrd and 4 textth fundamental modes of vibration?

Question

An organ pipe is closed at one end and open at the other. What is the ratio of frequencies of the 3 textrd and 4 textth fundamental modes of vibration? (A)  (3/4)  (B)  (5/7)  (C)  (3/5)  (D)  (9/11)

Tardigrade Admin · Accepted Answer

The frequency of 3 textrd fundamental mode of vibration. v3=(5 v/4 L) The frequency of 4 textth fundamental mode of vibration v4=(7 v/4 L) (v3/v4)=(5/7)

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

$\frac{3}{4}$

$\frac{5}{7}$

$\frac{3}{5}$

$\frac{9}{11}$

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

Q. An organ pipe is closed at one end and open at the other. What is the ratio of frequencies of the 3rd and 4th fundamental modes of vibration?

43​

75​

53​

119​