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

A standing wave produced on a string fixed at both ends has the equation y = (0.4 cm ) [(0.314 cm ⁻¹) x] [(600 s ⁻¹)t] . Determine the smallest possible length of the string.

Options

  1. A40 cm
  2. B10 cm
  3. C5 cm
  4. D20 cm

Correct answer

B. 10 cm

Step-by-step solution

The equation of the standing wave is given by y = A (kx) ( t) . Comparing the given equation with the standard form, we get k = 0.314 cm ⁻¹ . We know that k = 2 . 2 = 0.314 2 3.14 = 0.314 = 20 cm . For a string fixed at both ends, the length of the string must be an integral multiple of 2 . L = n 2 where n = 1, 2, 3, For the smallest possible length, n = 1 . L_ min = 2 = 20 2 = 10 cm .

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