The equation of a certain progressive transverse wave is y = 2 sin 2 \(\pi ( \frac{t}{0.01} - \frac{x}{30})\), where x and y are in cm and t in seconds. Cal...

The equation of a certain progressive transverse wave is y = 2 sin 2 \(\pi ( \frac{t}{0.01} - \frac{x}{30})\), where x and y are in cm and t in seconds. Calculate the period of the wave.

Answer Details

The general equation of a progressive transverse wave is given by: y = A sin (kx - ωt) where A is the amplitude, k is the wave number, x is the position of the particle, ω is the angular frequency, and t is the time. Comparing this equation with the given equation, we have: A = 2 cm k = 2π/30 cm^(-1) = π/15 cm^(-1) ω = 2π/T, where T is the period Thus, we have: ω = 2π/T = 2π/(0.01 s) Substituting the value of ω, we get: 2π/(0.01 s) = π/15 cm^(-1) Simplifying this equation, we get: T = 0.01 s Therefore, the period of the wave is 0.01 s.