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Concepts Of Physics MCQ Edition [Volume 1]PhysicsSound Waves

A copper rod of length 1.0 m is clamped at its middle point. Determine the frequencies between 20 Hz and 20 , 000 Hz at which standing longitudinal waves can be established in the rod. The speed of sound in copper is 3.8 km s ⁻¹ .

Options

  1. A3.8n kHz , where n = 1, 2, 3, 4, 5
  2. B1.9n kHz , where n = 1, 2, 3, , 10
  3. C1.9(2n - 1) kHz , where n = 1, 2, 3, 4, 5
  4. D1.9(2n - 1) kHz , where n = 1, 2, 3, , 10

Correct answer

C. 1.9(2n - 1) kHz , where n = 1, 2, 3, 4, 5

Step-by-step solution

The rod is clamped at its middle point, which means a node is formed at the center and antinodes are formed at the two free ends. The distance from the clamped center to either free end is L 2 . For standing waves, this distance must be an odd multiple of 4 . L 2 = (2n - 1) 4 = 2L 2n - 1 The corresponding frequencies are: f_n = v = (2n - 1)v 2L Substituting v = 3800 m s ⁻¹ and L = 1.0 m : f_n = (2n - 1) 3800 2 1.0 = 1900(2n - 1) Hz = 1.9(2n - 1) kHz The frequencies must lie between 20 Hz and 20 , 000 Hz ( 20 kHz ).

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