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Two waves are represented by the equations y1 = a sin (ωt + kx + 0.57) m and y2 = a cos (ωt + kx) m, where x is in meter and t in sec. The phase difference between them is [2011]
  • a)
    1.0 radian
  • b)
    1.25 radian
  • c)
    1.57 radian
  • d)
    0.57 radian
Correct answer is option 'A'. Can you explain this answer?
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Two waves are represented by the equations y1 = a sin (ωt + kx +...
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Two waves are represented by the equations y1 = a sin (ωt + kx +...
Ωt) and y2 = b sin (ωt + φ), where a, b, ω, and φ are constants.

The amplitude of the first wave is a, and the amplitude of the second wave is b.

The frequency of both waves is ω, which determines how many cycles of the wave occur per unit of time (usually seconds). The period of the wave is the time it takes for one complete cycle to occur, and is given by T = 2π/ω.

The phase difference between the two waves is φ, which determines how much the two waves are shifted in time relative to each other. If φ is positive, then y2 is shifted to the left (earlier in time) relative to y1. If φ is negative, then y2 is shifted to the right (later in time) relative to y1.

When the two waves are superimposed (added together), the resulting wave is given by y = y1 + y2. If the two waves are in phase (φ = 0), then the amplitude of the resulting wave is (a + b). If the two waves are out of phase (φ ≠ 0), then the amplitude of the resulting wave can be anywhere between (a - b) and (a + b), depending on the value of φ.
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Two waves are represented by the equations y1 = a sin (ωt + kx + 0.57) m and y2 = a cos (ωt + kx) m, where x is in meter and t in sec. The phase difference between them is [2011]a)1.0 radianb)1.25 radianc)1.57 radiand)0.57 radianCorrect answer is option 'A'. Can you explain this answer?
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