Question Detail

The general equation for a standing wave on a string fixed at both ends is y(x,t) = A_stand sin(kx) cos(ωt) (or sin(ωt)).From the previous problem: A_stand = 0.5 mm = 5.0 × 10⁻⁴ m.Wavelength λ = 5/9 m, so k = 2π/λ = 2π / (5/9) = 18π/5 rad/m.Frequency f = 450 Hz, so ω = 2πf = 2π * 450 = 900π rad/s.Substituting these values gives: y(x,t) = (5.0 × 10⁻⁴ m) sin((18π/5)x) cos(900πt).(Note: The choice between sin(ωt) or cos(ωt) depends on the exact initial phase, but cos(ωt) is a common form if the wave is at maximum displacement at t=0.)