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MHT CET20249 May 2024Evening ShiftPhysicsWaves and SoundActual

The equations of two waves are given as aligned & y ₁= asin ( t + ₁ ) & y ₂= asin ( t + ₂ ) aligned If amplitude and time period of resultant wave is same as the individual waves, then ( ₁- ₂ ) is

Options

  1. A⁻¹ ( -1 2 )
  2. B⁻¹ ( -1 4 )
  3. C⁻¹ (- 1 6 )
  4. D⁻¹ (- 1 8 )

Correct answer

A. ⁻¹ ( -1 2 )

Step-by-step solution

aligned & y ₁= a ( t + ₁ ) & y ₂= asin ( t + ₂ ) ...(i) aligned Superposition of two waves is given by a^2=a₁^2+a₂^2+2 a₁ a₂ ...(ii) Here, = ₁- ₂ and a₁=a₂=a Substituting these values in equation (i), we get, aligned & ( ₁- ₂ )=- 1 2 & ( ₁- ₂ )= ⁻¹ ( -1 2 ) aligned

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