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

A wave is described by the equation y = (0.001 mm ) [(50 s ⁻¹)t + (2.0 m ⁻¹)x] .

Options

  1. AThe wavelength is 2.0 m
  2. BThe frequency is 25/ Hz
  3. CThe amplitude is 0.001 mm
  4. DThe wave velocity is 100 m s ⁻¹

Correct answer

C. The amplitude is 0.001 mm

Step-by-step solution

The given wave equation is y = (0.001 mm ) [(50 s ⁻¹)t + (2.0 m ⁻¹)x] Comparing this with the standard wave equation y = A ( t + kx) , we get: Amplitude A = 0.001 mm Angular frequency = 50 rad s ⁻¹ Wave number k = 2.0 m ⁻¹ The wavelength is given by = 2 k = 2 2.0 = m The frequency is given by f = 2 = 50 2 = 25 Hz The wave velocity is given by v = k = 50 2.0 = 25 m s ⁻¹ Thus, the frequency is 25/ Hz and the amplitude is 0.001 mm .

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