Question

When an air column in a pipe closed at one end vibrates such that two nodes are formed in it, the frequency of its vibration is ______.

विकल्प

• two times the fundamental frequency

• three times the fundamental frequency

• four times the fundamental frequency

• five times the fundamental frequency

Answer 1

When an air column in a pipe closed at one end vibrates such that two nodes are formed in it, the frequency of its vibration is three times the fundamental frequency.

Explanation:

In a pipe that is closed at one end, only odd harmonics are produced—such as the 1st, 3rd, and 5th. The fundamental frequency (1st harmonic) has one node at the closed end and one antinode at the open end. When two nodes are formed, the standing wave represents the third harmonic, which has two nodes and two antinodes. The frequency of the third harmonic is three times the fundamental frequency. Therefore, the formation of two nodes in such a pipe results in a vibration frequency that is three times the fundamental frequency.