Question

33. Write the mathematical equation to represent a wave.
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Answer 1

Answer:

"Taking the ratio and using the equation v=ω/k v = ω / k yields the linear wave equation (also known simply as the wave equation or the equation of a vibrating string), ∂2y(x,t)∂t2∂2y(x,t)∂x2=−Aω2sin(kx−ωt+φ)−Ak2sin(kx−ωt+φ)=ω2k2=v2, ∂2y(x,t)∂x2=1v2∂2y(x,t)∂t2. ∂ 2 y ( x , t ) ∂ x 2 = 1 v 2 ∂ 2 y ( x , t ) ∂ t 2 ."