Final answer:
The equation for the displacement of the wave is d(x,t) = (3.5 cm) sin(3.0x - 122t). The amplitude determines the maximum displacement of the wave, while the phase determines the position and time dependence of the wave.
Step-by-step explanation:
The equation for the displacement of the wave is d(x,t) = (3.5 cm) sin((3.0x - 122t)).
In this equation, d(x,t) represents the displacement of the wave at a certain position (x) and time (t). The 3.5 cm is the amplitude of the wave, which determines the maximum displacement of the wave from its equilibrium position. The 3.0x - 122t term represents the phase of the wave, which determines the position and time dependence of the wave. The sin function relates the phase to the displacement. This equation embodies the intricate relationship between spatial and temporal variables, elucidating how waves propagate and manifest their amplitude and phase as they traverse through space and time.