Final answer:
To find the amplitude, period, phase shift, and other characteristics of a sinusoidal wave, use the terms in the wave equation y(x, t) = A sin(kx - ωt + p). The amplitude is A, the period T is computed using T = 2π/ω, and the phase shift is represented as p. The frequency f is the reciprocal of the period, and the wavelength is calculated using λ = 2π/k.
Step-by-step explanation:
To find the amplitude, period, and phase shift of a wave, you can use the standard form of the sinusoidal wave function y (x, t) = A sin (kx - ωt + p), where:
- A is the amplitude of the wave, representing the maximum displacement from the rest position.
- The period (T) can be calculated from the angular frequency using the formula T = 2π/ω.
- The phase shift is indicated by p in the equation and represents the horizontal shift of the wave.
- The frequency (f) is the reciprocal of the period, f = 1/T.
- The wavelength (λ) is related to the wave number (k) by the formula λ = 2π/k.
To calculate the amplitude of the wave, look directly at the coefficient A in front of the sine function in the wave equation. For example, for the wave equation y (x, t) = 0.2 m sin (6.28 m¯¹x - 1.57 s¯¹t), the amplitude would be 0.2 m.
To show the period of the wave, you would take the angular frequency (ω) from the equation and use the formula for period: T = 2π/ω.
The frequency is then calculated by taking the reciprocal of the period, and the velocity (v) of the wave can be determined by the product of the frequency and the wavelength, v = f λ.