The particle displacement in a simple harmonic wave is given by
y(x, t) = 2 sin 4$\pi$(t + x/8),
Where the units are SI. A graph of particle displacement as a function of position at
T = 0.5s would include points
A) A and D
B) B and D
C) C and E
D) B and E
E) D and F

Question

The particle displacement in a simple harmonic wave is given by 
y(x, t) = 2 sin 4$\pi$(t + x/8),
Where the units are SI. A graph of particle displacement as a function of position at
T = 0.5s would include points
A) A and D 
B) B and D 
C) C and E 
D) B and E 
E) D and F

Quizplus · Accepted Answer

At t=0.5s, the argument of the sine function becomes 4π/2 = 2π.
Hence, the equation of the wave becomes y(x,0.5) = 2sin(2π + x/8).
To find the positions where the particle displacement is maximum, we need to find the values of x for which sin(2π + x/8) = ±1.
For sin(2π + x/8) = 1, we get x/8 = (4nπ + π/2 - 2π) where n is an integer.
Solving for x, we get x = 8[(4n-3)/8]π, where n is an integer. This gives us the positions D and E.
For sin(2π + x/8) = -1, we get x/8 = (4nπ + 3π/2 - 2π) where n is an integer.
Solving for x, we get x = 8[(4n-1)/8]π, where n is an integer. This gives us the positions B and F.
Therefore, the correct choice is D.

The Particle Displacement in a Simple Harmonic Wave Is Given π\piπ

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