Question

In an open end organ pipe of length 'L', if the velocity of sound is 'V', then the fundamental frequency will be (Neglect end correction) ______.

• A. $\frac{V}{2L}$ and all harmonics are present.
• B. $\frac{V}{4L}$ and all harmonics are present.
• C. $\frac{V}{2L}$ and even harmonics are present.
• D. $\frac{V}{4L}$ and even harmonics are present.

Hint:

Open pipes sound richer and more musical than closed pipes specifically because they produce all harmonics, providing a fuller overtone spectrum.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
An open organ pipe has antinodes at both ends. The fundamental mode of vibration corresponds to the longest wavelength that can fit these boundary conditions.

Step 2: Formula Application:
For the fundamental mode, the length $L$ is equal to half the wavelength ($\lambda/2$). Therefore, $\lambda = 2L$. Fundamental frequency $n = V / \lambda = V / 2L$.

Step 3: Explanation:
In an open pipe, the successive harmonics are integral multiples of the fundamental frequency ($n, 2n, 3n, \dots$). This means both odd and even harmonics (all harmonics) are present in the vibration.

Step 4: Final Answer:
The frequency is $V/2L$ and all harmonics are present.