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

Two waves, each possessing a frequency of 100 Hz , a wavelength of 2.0 cm , and an amplitude of 2.0 mm , travel in the same direction on a string. Determine the phase difference and the resultant wave amplitude for the following two scenarios: First scenario: The second wave is produced 0.015 s later than the first wave at the identical location. Second scenario: Both waves are produced simultaneously, while the firs

Options

  1. AFirst scenario: 4 rad , 4.0 mm ; Second scenario: 3 rad , 0 mm
  2. BFirst scenario: 3 rad , 4.0 mm ; Second scenario: 4 rad , 0 mm
  3. CFirst scenario: 1.5 rad , 0 mm ; Second scenario: 2 rad , 4.0 mm
  4. DFirst scenario: 3 rad , 0 mm ; Second scenario: 4 rad , 4.0 mm

Correct answer

D. First scenario: 3 rad , 0 mm ; Second scenario: 4 rad , 4.0 mm

Step-by-step solution

Given f = 100 Hz , = 2.0 cm , A = 2.0 mm . For the first scenario, the time difference is t = 0.015 s . The phase difference due to the time difference is ₁ = 2 f t . ₁ = 2 100 0.015 = 3 rad The resultant amplitude is A_ R1 = A^2 + A^2 + 2A^2 ( ₁) . A_ R1 = 2A^2 + 2A^2 (3 ) = 2A^2 - 2A^2 = 0 mm For the second scenario, the path difference is x = 4.0 cm . The phase difference due to the path difference is ₂ = 2 x . ₂ = 2 2.0 4.0 = 4 rad The resultant amplitude is A_ R2 = A^2 + A^2 + 2A^2 ( ₂) . A_ R2 = 2A^2 + 2A^2 (

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