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 ______.

Options

• 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 five times the fundamental frequency.

Explanation:

In a pipe closed at one end, only odd harmonics are formed (i.e., 1st, 3rd, 5th…). The fundamental mode (first harmonic) has 1 node and 1 antinode. When 2 nodes are formed, the standing wave pattern corresponds to the third mode of vibration, which is the fifth harmonic component in terms of segments.