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. The speed of the wave is

Question

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. The speed of the wave is, 8 m s - 1, 4 π m s - 1, 0.5 π m s - 1, π 4 m s - 1

MARKS App · Accepted Answer

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

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