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A sinusoidal wave (longitudinal or transverse) is propagating through a medium in the direction of -ve x-axis. The parameters of the waves are A, ω and k. The particle at x = λ/4 executes the motion y(t) = A sinωt. Possible equation of the wave is
  • a)
    y(x, t) = A sin[ωt - kx + (π/2)]
  • b)
    y(x, t) = A sin[ωt + kx + (π/2)]
  • c)
    y(x, t) = A sin[ωt - kx - (π/2)]
  • d)
    y(x, t) = A sin[ωt + kx - (π/2)]
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A sinusoidal wave (longitudinal or transverse) is propagating through ...
Let equation of wave as it is moving along - ve x-axis is y = A sin(kx + ωt +α) But, y(λ/4, t) = A sinωt Comparing then kx + α = 0 ⇒ a =-π/2
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A sinusoidal wave (longitudinal or transverse) is propagating through ...
Λ, ω, and φ. The amplitude (A) represents the maximum displacement of particles in the medium from their equilibrium position. The wavelength (λ) is the distance between two consecutive points in the wave that are in phase. The angular frequency (ω) represents the rate at which the wave oscillates and is related to the period (T) of the wave by the equation ω = 2π/T. The phase constant (φ) represents the initial phase of the wave at t = 0.

The equation for the sinusoidal wave can be written as:
y(x, t) = A*sin(kx - ωt + φ)

Where y(x, t) represents the displacement of particles in the medium at position x and time t, k = 2π/λ is the wave number, and ω is the angular frequency.

Since the wave is propagating in the direction of the -ve x-axis, the wave equation can be written as:
y(x, t) = A*sin(-kx - ωt + φ)

In this case, the negative sign in front of kx indicates that the wave is traveling in the opposite direction of the positive x-axis.
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A sinusoidal wave (longitudinal or transverse) is propagating through a medium in the direction of -ve x-axis. The parameters of the waves are A, ω and k. The particle at x = λ/4 executes the motion y(t) = A sinωt. Possible equation of the wave isa)y(x, t) = A sin[ωt - kx + (π/2)]b)y(x, t) = A sin[ωt + kx + (π/2)]c)y(x, t) = A sin[ωt - kx - (π/2)]d)y(x, t) = A sin[ωt + kx - (π/2)]Correct answer is option 'D'. Can you explain this answer?
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A sinusoidal wave (longitudinal or transverse) is propagating through a medium in the direction of -ve x-axis. The parameters of the waves are A, ω and k. The particle at x = λ/4 executes the motion y(t) = A sinωt. Possible equation of the wave isa)y(x, t) = A sin[ωt - kx + (π/2)]b)y(x, t) = A sin[ωt + kx + (π/2)]c)y(x, t) = A sin[ωt - kx - (π/2)]d)y(x, t) = A sin[ωt + kx - (π/2)]Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A sinusoidal wave (longitudinal or transverse) is propagating through a medium in the direction of -ve x-axis. The parameters of the waves are A, ω and k. The particle at x = λ/4 executes the motion y(t) = A sinωt. Possible equation of the wave isa)y(x, t) = A sin[ωt - kx + (π/2)]b)y(x, t) = A sin[ωt + kx + (π/2)]c)y(x, t) = A sin[ωt - kx - (π/2)]d)y(x, t) = A sin[ωt + kx - (π/2)]Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sinusoidal wave (longitudinal or transverse) is propagating through a medium in the direction of -ve x-axis. The parameters of the waves are A, ω and k. The particle at x = λ/4 executes the motion y(t) = A sinωt. Possible equation of the wave isa)y(x, t) = A sin[ωt - kx + (π/2)]b)y(x, t) = A sin[ωt + kx + (π/2)]c)y(x, t) = A sin[ωt - kx - (π/2)]d)y(x, t) = A sin[ωt + kx - (π/2)]Correct answer is option 'D'. Can you explain this answer?.
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