Final answer:
The wave properties such as amplitude, wavelength, velocity, and period can be determined from wave functions like y(x, t) = A sin(kx - ωt + p). Instantaneous velocity can be found using calculus, whereas average velocity requires the displacement over a time interval. The period is the inverse of the frequency (T = 1/f).
Step-by-step explanation:
To determine various properties of a wave, such as amplitude, wavelength, velocity, period, and how many crests pass an observer, we analyze the wave functions provided. A wave function like y(x, t) = A sin(kx - ωt + p) encapsulates all these properties. Here, A represents the amplitude, k is the wave number (which is related to wavelength λ by k = 2π/λ), ω is the angular frequency (related to the period T by ω = 2π/T), and p is the phase shift. The constant velocity v of the wave can be calculated using the relationship v = λ/T. When evaluating the wave at specific times, we can compare two functions at t = 0.00 s and t = 2.00 s, as shown by the dotted and solid lines, to estimate the mentioned properties.
For the instantaneous velocity at a specific time, we can use the derivative of the wave function with respect to time. The average velocity between two time intervals is found by taking the difference of the displacement and dividing it by the time elapsed. Additionally, to find the period given the frequency, we use the formula T = 1/f.