A sinusoidal wave travelling in the positive direction on stretched string has amplitude 2.0 cm, wavelength 1.0 m and wave velocity 5.0 m/s. At x = 0 and t = 0 it is given that y = 0 and ∂y/∂t<0. Find the wave function y(x, t).

We start with a general form for a rightward moving wave, y(x,t)=Asin⁡(kx−ωt+ϕ)The amplitude given is A=2.0cm=0.02m.The wavelength is given as, λ=1.0mWave number =k=2π/λ=2πm−1Angular frequency, ω=kv=2π×5=10π rad/sy(x,t)=(0.02)sin⁡[2π(x−5.0t)+ϕ]       y=0 and ∂y∂t<0i.e., 0.02sin⁡ϕ=0     (as y=0)and −0.2πcos⁡ϕ<0From these conditions, we may conclude thatϕ=2nπ  where  n=0,2,4,6,…Therefore, y(x,t)=(0.02m)sin⁡2πm−1x−10πs−1tm