A wave propagates on a string in the positive x-direction at a velocity v. The shape of the string at t = t₀ is given by g(x,t₀) = Asin(x/a). Write the wave equation for a general time t.
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A progressive wave going in direction +x.
velocity = v
Shape at the initial time t₀ is g(x, t₀) = A Sin (x/a)
General Wave equation for a progressive wave at x at time t:
g (x, t) = A Sin(ωt - k x) = A Sin [ω(t - x/v)] = A Sin [2π(t/T - x/λ)]
At time t₀ then g(x, t₀) = A Sin (ω t₀ - k x) = A Sin (x/a) given
=> ωt₀ = π. k = 1/a
As k = ω/v , ω = k v = 1/a * v = v/a
Equation of the wave : g(x,t) = A Sin (v t / a - x/a )
= A Sin [(v t - x)/a ]
velocity = v
Shape at the initial time t₀ is g(x, t₀) = A Sin (x/a)
General Wave equation for a progressive wave at x at time t:
g (x, t) = A Sin(ωt - k x) = A Sin [ω(t - x/v)] = A Sin [2π(t/T - x/λ)]
At time t₀ then g(x, t₀) = A Sin (ω t₀ - k x) = A Sin (x/a) given
=> ωt₀ = π. k = 1/a
As k = ω/v , ω = k v = 1/a * v = v/a
Equation of the wave : g(x,t) = A Sin (v t / a - x/a )
= A Sin [(v t - x)/a ]
kvnmurty:
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