Concepts Of Physics MCQ Edition [Volume 1]PhysicsWave Motion and Waves on a String

A standing wave is established on a string that is clamped at one end and free at the opposite end. The length of the string

Options

Amust be an integral multiple of 4
Bmust be an integral multiple of 2
Cmust be an integral multiple of
Dmay be an integral multiple of 2

Correct answer

A. must be an integral multiple of 4

Step-by-step solution

For a string clamped at one end and free at the other end, a node is formed at the clamped end and an antinode is formed at the free end. The distance between a node and the adjacent antinode is 4 . The length of the string L is given by L = (2n - 1) 4 , where n = 1, 2, 3, Since (2n - 1) is an integer, the length of the string must be an integral multiple of 4 .

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