Question

When open pipe is closed from one end then third overtone of closed pipe is higher in frequency by 150 Hz than second overtone of open pipe. The fundamental frequency of open end pipe will be

• A. 300 Hz
• B. 500 Hz
• C. 200 Hz
• D. 400 Hz

Hint:

In pipes, the overtone frequencies for open and closed pipes follow different series based on whether the pipe is open at both ends or closed at one end.

Answer 1

The Correct Option is A

Step 1: Relation between overtone frequencies.
For a closed pipe, the overtones are given by odd multiples of the fundamental frequency. For an open pipe, the overtones are given by integer multiples. Given that the third overtone of the closed pipe is 150 Hz higher than the second overtone of the open pipe, we can find the fundamental frequency.
Step 2: Calculation.
Let the fundamental frequency of the open pipe be \( f_1 \). From the relationship between the overtones and fundamental frequency, the difference in frequencies leads us to the conclusion that the fundamental frequency of the open pipe is \( 300 \, \text{Hz} \).
Step 3: Conclusion.
Thus, the correct answer is (A) 300 Hz.