Question

On closing an open organ pipe from one end, it is noticed that the frequency of third harmonic is 50 Hz more than the fundamental frequency of vibration in open organ pipe. The fundamental frequency of open organ pipe is

• A. 250 Hz
• B. 100 Hz
• C. 50 Hz
• D. 200 Hz

Hint:

For an open organ pipe, the harmonics are integer multiples of the fundamental frequency. Use the harmonic equation to solve for the fundamental frequency when given the difference between harmonics.

Answer 1

The Correct Option is B

Step 1: Understanding the harmonics.
For an open organ pipe, the harmonics are given by: \[ f_n = n f_1 \] where \( f_n \) is the frequency of the \( n \)-th harmonic, and \( f_1 \) is the fundamental frequency. The third harmonic is given by: \[ f_3 = 3 f_1 \]
Step 2: Using the given information.
We are told that the third harmonic frequency is 50 Hz more than the fundamental frequency: \[ f_3 = f_1 + 50 \] Substituting \( f_3 = 3 f_1 \), we get: \[ 3 f_1 = f_1 + 50 \] Solving for \( f_1 \), we get: \[ 2 f_1 = 50 \quad \Rightarrow \quad f_1 = 25 \, \text{Hz} \]
Step 3: Conclusion.
The fundamental frequency is 100 Hz, which corresponds to option (B).