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Waves question

2001 · Q164
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Waves question

2001 · Q164

NEETPhysicsWavesMCQ+4 / −1
Two waves having equation x1 = aaasin(ω\omegaωt −-− kx + ϕ\phiϕ1), x2 = asin(ω\omegaωt −-−kx + ϕ\phiϕ2). If in the resultant wave the frequency and amplitude remain equal to amplitude of superimposing waves, the phase difference between them is
  1. A
    π6{\pi \over 6}6π​
  2. B
    2π3{{2\pi } \over 3}32π​
  3. C
    π4{\pi \over 4}4π​
  4. D
    π3{\pi \over 3}3π​
View written solutionFree

Correct answer: B

Resultant amplitude = 2a (1 + cosϕ\phi ϕ) = a

∴\therefore∴ (1+cos⁡ϕ)=1/2;\left( {1 + \cos \phi } \right) = 1/2;(1+cosϕ)=1/2;

cosϕ=−12;ϕ=2π3cos\phi = - {1 \over 2};\phi = {{2\pi } \over 3}cosϕ=−21​;ϕ=32π​

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