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 solve the problem of determining the ratio of frequencies of the fundamental harmonic produced by an open pipe to that of a closed pipe having the same length, we need to use the basic formulae for calculating the fundamental frequency in both scenarios.

Step 1: Understand the concept

An open pipe can produce harmonics at all multiples of the fundamental frequency, while a closed pipe produces only odd multiples of its fundamental frequency.

Step 2: Fundamental frequency formulae

• For an open pipe: The fundamental frequency is given by \(f_o = \frac{v}{2L}\), where \(v\) is the speed of sound in air and \(L\) is the length of the pipe.
• For a closed pipe: The fundamental frequency is given by \(f_c = \frac{v}{4L}\).

Step 3: Calculate the ratio

The ratio of the fundamental frequency of the open pipe (\(f_o\)) to that of the closed pipe (\(f_c\)) is:

\(\text{Ratio} = \frac{f_o}{f_c} = \frac{\frac{v}{2L}}{\frac{v}{4L}} = \frac{4L}{2L} = \frac{4}{2} = 2:1\)

Conclusion

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