Final answer:
The equation represents a standing wave with an antinode. The radii of motion for two particles is 4 units. The given wave equation has an angular frequency, wave number, amplitude, and phase shift.
Step-by-step explanation:
The equation y(x, t) = 4.00 cm sin (3 m¯¹x + 2) cos (4 s¯¹t) represents a standing wave. When the value of x is 0.00 m, the sine term becomes 0.00 and the cosine term oscillates between +1 and -1, creating an antinode where the amplitude of y oscillates between +A and -A. The value of A represents the amplitude of the wave.
The radii of the circles of motion of the particles in the given equations 4 cos(2t) and 4 sin(2t) are both 4 units. The x-coordinate of the center of mass of these particles is 0 and the y-coordinate is also 0, as the sum of the sines and cosines is 0.
The given equation YR(x, t) = 0.70 m sin (3.00 m¯¹x - 6.28 s¯¹t+ T/16 rad) represents a wave. The angular frequency is 6.28 rad/s, the wave number is 3.00 m¯¹, the amplitude is 0.70 m, and the phase shift is T/16 rad.