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

A string of length L secured at both ends vibrates in its fundamental mode with a frequency u and a maximum amplitude A . Determine the wavelength and the wave number k .

Options

  1. AL and 2 L
  2. BL 2 and 4 L
  3. C2L and 2 L
  4. D2L and L

Correct answer

D. 2L and L

Step-by-step solution

For a string of length L secured at both ends, the fundamental mode of vibration consists of a single loop. The distance between two consecutive nodes is 2 . Since the string is fixed at both ends, the length of the string is equal to half the wavelength. L = 2 = 2L The wave number k is defined as: k = 2 Substituting = 2L : k = 2 2L = L Thus, the wavelength is 2L and the wave number is L .

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