Question

The ratio of frequencies of fundamental harmonic produced by an open pipe to that of closed pipe having the same length is:

• A. 3:1
• B. 1:2
• C. 2:1
• D. 1:3

Answer 1

The Correct Option is C

To understand the problem, we need to analyze how the fundamental frequencies of open and closed pipes relate. An open pipe resonates at a fundamental frequency \( f_{\text{open}} \) given by:

\( f_{\text{open}} = \frac{v}{2L} \)

 

where \( v \) is the speed of sound in air and \( L \) is the length of the pipe.

For a closed pipe (open at one end and closed at the other), the fundamental frequency \( f_{\text{closed}} \) is:

\( f_{\text{closed}} = \frac{v}{4L} \)

 

Comparing these two equations, the ratio of the fundamental frequencies is:

\(\frac{f_{\text{open}}}{f_{\text{closed}}} = \frac{\frac{v}{2L}}{\frac{v}{4L}} = \frac{4L}{2L} = 2\)

 

Thus, the ratio of the frequencies of the fundamental harmonic produced by an open pipe to that of a closed pipe of the same length is 2:1.