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Concepts Of Physics MCQ Edition [Volume 1]PhysicsSound Waves

In a Kundt's tube apparatus, a steel rod of length 1.0 m is clamped at its centre. It is set into vibration in its fundamental mode with a frequency of 2600 Hz . The lycopodium powder dispersed inside the tube gathers into heaps that are separated by 6.5 cm . Determine the speed of sound in steel and in air, respectively.

Options

  1. A2600 m/s and 338 m/s
  2. B5200 m/s and 338 m/s
  3. C5200 m/s and 169 m/s
  4. D2600 m/s and 169 m/s

Correct answer

B. 5200 m/s and 338 m/s

Step-by-step solution

For the steel rod clamped at the centre and vibrating in its fundamental mode, the centre is a node and the ends are antinodes. Length of the rod, L = _ steel 2 _ steel = 2L = 2 1.0 = 2.0 m Speed of sound in steel, v_ steel = f _ steel = 2600 2.0 = 5200 m/s In the Kundt's tube, the distance between consecutive heaps of lycopodium powder represents the distance between consecutive nodes of the standing wave in air. _ air 2 = 6.5 cm = 0.065 m _ air = 2 0.065 = 0.13 m Speed of sound in air, v_ air = f _ air = 2600 0.1

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