Final answer:
The wave equation Y=A sin 2π(0.15t-0.1x) indicates a period of 6.67 s, frequency of 0.15 Hz, wavelength of 62.83 m, and velocity of 9.425 m/s. These values were extracted by comparing the given wave equation to the standard wave equation form.
Step-by-step explanation:
The progressive wave equation given is represented by Y=A sin 2π(0.15t-0.1x), where A is the amplitude, t is time, and x is the position. The general form of a wave equation is Y=A sin 2π(ft - (x/λ)), where f is the frequency and λ (lambda) is the wavelength. By comparing the two, we can extract information about the period, frequency, wavelength, and velocity of the wave.
1. The period (T)
The period of the wave is the reciprocal of the frequency. From the equation, the coefficient of t is the frequency (f = 0.15 Hz), so the period T = 1/f, which is T = 1/0.15 s or T = 6.67 s.
2. The frequency (f)
The frequency is already given by the coefficient of t in the equation, which is f = 0.15 Hz.
3. Wavelength (λ)
The wavelength is determined by the coefficient of x in the equation. This is the wave number k = 2π/λ. Therefore, k is 0.1, which gives λ = 2π/0.1 m or λ = 62.83 m.
4. Velocity (v)
The velocity of the wave is the product of its frequency and wavelength, v = f * λ. Substituting the known values, we get v = 0.15 Hz * 62.83 m, which yields the velocity v = 9.425 m/s.