A transverse wave propagating along the x -axis is represented by y ( x , t ) = 8 . 0 sin ( 0 . 5 π x – 4 π t – π 4 ) where x is in metres and t is in seconds. What is the speed (in m s - 1 ) of the wave?

Step-by-step solution

y x t = 8 · 0 sin 0 · 5 π x - 4 π t - π 4 Compare with a standard wave equation, y = a sin 2 π x λ - 2 π t T ⁡ + ϕ we get  2 π λ = 0 · 5 π or, λ = 2 π 0 · 5 π = 4 m 2 π T ⁡ = 4 π or, T ⁡ = 2 π 4 π = 1 2   s υ = 1 / T = 2 Hz Wave velocity, ν = λ υ = 4 × 2 = 8 m s - 1