Question

The third overtone of a closed pipe is in unison with the second overtone of an open pipe. Hence the ratio of the length of the closed pipe to that of the open pipe is:

• A. 1 : 2
• B. 6 : 7
• C. 7 : 6
• D. 3 : 2

Hint:

The overtone frequencies in closed and open pipes are related by the harmonic series, and the relationship of their lengths can be derived based on these series.

Answer 1

The Correct Option is D

Step 1: Understanding the relationship.
In the case of a closed pipe and an open pipe, the overtones are related to their respective fundamental frequencies. The length of the closed pipe is shorter compared to the open pipe to produce the same overtone.
Step 2: Conclusion.
The ratio of the lengths of the closed pipe to the open pipe is found to be \( 3 : 2 \).