A sinusoidal wave is described by y = A sin(kx-ωt). At a fixed position x, what is the instantaneous transverse velocity uᵧ of the particle of the medium?
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Question

A sinusoidal wave is described by y = A sin(kx−ωt). At a fixed position x, what is the instantaneous transverse velocity uᵧ of the particle of the medium?

G1 Physics · Accepted Answer

Particle velocity is obtained by differentiating displacement with respect to time at fixed x: uᵧ = ∂y/∂t. Therefore, uᵧ = ∂/∂t [A sin(kx−ωt)] = −Aω cos(kx−ωt). Correct option: B.