A wave is represented by y = 0.01 sin(πx−20t), where all quantities are in SI units. At a certain instant a particular particle of the medium has displacement 5 mm. If the magnitude of its transverse acceleration is N m/s², find N.
Physics · Wave Motion · general equation of wave
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Question

A wave is represented by y = 0.01 sin(πx−20t), where all quantities are in SI units. At a certain instant a particular particle of the medium has displacement 5 mm. If the magnitude of its transverse acceleration is N m/s², find N.

Physics · Wave Motion · general equation of wave

G1 Physics · Accepted Answer

For every particle of a sinusoidal travelling wave, aᵧ = −ω²y. Here, ω = 20 rad/s, |y| = 5 mm = 5×10⁻³ m. Therefore, |aᵧ| = 20²×5×10⁻³ = 400×0.005 = 2 m/s². Hence, N = 2.