What if one end of an 11 meter organ pipe was covered?

If one end of an 11-meter organ pipe is covered, it becomes what's known as a closed organ pipe. Closed pipes have one closed and one open end. The covered end acts as a closed node, while the open end acts as an anti-node.

As a result, the lowest resonant frequency of the pipe decreases. The formula for the resonant frequency of a closed pipe is:

f = (v/4L)

Where:

f = Resonant frequency

v = Speed of sound (approximately 343 m/s at room temperature)

L = Length of the pipe

With one end closed, the effective length of the pipe for the lowest resonant frequency becomes half the actual length. So, for an 11-meter organ pipe with one end closed, the lowest resonant frequency becomes:

f = (343 m/s / (4 x 5.5 m)) ≈ 15.6 Hz

This means the fundamental frequency or the first harmonic of the pipe is approximately 15.6 Hz when one end is closed. The other resonant frequencies or overtones also change accordingly, resulting in a different harmonic series compared to an open pipe of the same length.

Closed organ pipes have a characteristic mellow and flute-like sound quality, and they are commonly used in pipe organs and other musical instruments.