A plane progressive wave is described by y = 5 cos{π[200t-(x / 150)]}, where x and y are measured in centimetres and t in seconds. What is the speed of the wave in m·s⁻¹?
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A plane progressive wave is described by y = 5 cos{π[200t-(x / 150)]}, where x and y are measured in centimetres and t in seconds. What is the speed of the wave in m·s⁻¹?

G1 Physics · Accepted Answer

Compare the given wave with the standard phase form y = A cos(ωt-kx). The coefficient of t inside the phase is 200π, and the coefficient of x is π ÷ 150 per centimetre. Therefore the wave speed in centimetres per second is v = ω ÷ k = (200π) ÷ (π ÷ 150) = 200×150 = 30000 cm·s⁻¹. Converting to metres per second: 30000 cm·s⁻¹ = 300 m·s⁻¹. Correct option: D.