A 2.23-Hz simple harmonic wave is propagating in the negative x-direction at 35.0 cm/s, with amplitude 2.87 cm.?

sin(0) = 0 (so wave has zero displacement when x=0 and t=0)

cos(0) = 1 (so wave has max. displacement when x=0 and t=0)

Since the displacement at x = 0 is maximum when t = 0, we use cosine. (We could use sine but then we would need to add a fixed phase angle.)

For a wave moving in the +x direction: y(x, t) = Acos(kx - ωt) (equation 1)

For a wave moving in the -x direction: y(x, t) = Acos(kx + ωt) (equation 2)

λ = v/f = 35.0/2.23 = 15.695cm

k = 2π/λ = 2π/15.695 = 0.400 cm⁻¹

ω = 2πf = 2π x 2.23 = 14.0 rad/s

So using equation 2 gives:

y(x,t) = 2.87cos(0.400x + 14.0t)

35 cm/s = 0.35m/s

λ = v/f = 0.35/2.23 = 0.156 m

k = 2π/λ = 2π/15.695 = 40 m⁻¹

ω = 2πf = 2π x 2.23 = 14 rad/s

y(x,t) = 2.87cos(40x + 14t)