For the progressive wave y = A sin(kx−ωt), which expression gives the transverse acceleration aᵧ of a particle of the medium at displacement y?
Physics · Wave Motion · general equation of wave
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Question

For the progressive wave y = A sin(kx−ωt), which expression gives the transverse acceleration aᵧ of a particle of the medium at displacement y?

G1 Physics · Accepted Answer

At a fixed x, the particle performs SHM. Differentiate twice with respect to time: aᵧ = ∂²y/∂t² = −ω²A sin(kx−ωt). Since y = A sin(kx−ωt), we obtain aᵧ = −ω²y. Correct option: A.