Final answer:
To find a wave's amplitude, period, and phase shift, use the wave equation y(x, t) = A sin(kx - wt + φ). Amplitude is A, period is 2π / w, phase shift is the constant φ, and frequency is w / 2π.
Step-by-step explanation:
When analyzing a sinusoidal wave, such as y(x, t) = A sin(kx - wt + φ), where A is the amplitude, k represents the wave number, w the angular frequency, and φ the phase shift, we use specific parts of this equation to find the wave's characteristics.
The amplitude is the distance between the wave's resting position and its maximum displacement, and we can determine it directly as the absolute value of A in the equation.
The period of the wave (T) represents the time it takes for one wave cycle to complete. It can be calculated using T = 2π / w.
To find the phase shift, we look at the constant φ within the equation. If the wave equation is A sin(kx - wt) there is no phase shift.
The frequency of the wave (f), the number of waves passing by a specific point per second, is found using the relation f = w / 2π.