Question

An organ pipe open at both the ends has its fundamental frequency 200 Hz. If one end of it is closed and the other end is kept open, the frequencies produced by it are

• A. 200 Hz, 400 Hz, 600 Hz, 800 Hz....
• B. 200 Hz, 300 Hz, 400 Hz, 500 Hz....
• C. 100 Hz, 300 Hz, 500 Hz, 700 Hz....
• D. 100 Hz, 200 Hz, 300 Hz, 400 Hz....
• E. 200 Hz, 250 Hz, 300 Hz, 350 Hz....

Hint:

An open pipe has all harmonics; a closed pipe has only odd harmonics.

Answer 1

The Correct Option is C

Step 1: Concept
The fundamental frequency of an open pipe is $f_{open} = \frac{v}{2L}$ and for a closed pipe is $f_{closed} = \frac{v}{4L}$.

Step 2: Meaning
Closing one end of an open pipe halves its fundamental frequency.

Step 3: Analysis
New fundamental frequency $= 200 / 2 = 100$ Hz. Closed pipes produce only odd harmonics ($1f, 3f, 5f...$).

Step 4: Conclusion
The frequencies are 100 Hz, 300 Hz, 500 Hz, etc.
Final Answer: (C)