What is the equation for the wave?

Question

A wave has the following properties:amplitude=0.575 m, period=0.730 s, wave speed=14.4 m/s. The wave is traveling in the -x direction.

Answer 1

Answer 1 provides a t-only response and an x-only response. Such an analysis could apply to a standing wave, but is unrealistic for a traveling wave. The displacement amplitude y at any point on the string is a function of both position x and time t. In other words, y is expressed as y(x,t).
Say the wave at a reference point (x=0) is defined as
a cosine wave per answer 1:
y(0,t) = A * cos(omega * t).
Then we have a time lag deltaT at position x represented by x / wave speed V. So the wave amplitude at x is
y(x,t) = A * cos(omega * (t - x/V))
Since the wave propagates in the -x direction we have to change the sign of the x term:
y(x,t) = A * cos(omega * (t + x/V))
As applied to this system, the numeric formula is
y(x,t) = 0.575 * cos(8.607 * (t + x/14.4))

Answer 2

2 answers; one involving t, one not.

a) ω = 2π/T = 2π/.73 = 8.607 rad/sec in which case y = .575*cos(8.607*t)

b) λ = s*T = 14.4*.73 = 10.512 m and θ = 2πx/λ = 2πx/10.512 = .5977*x. In these terms, y = .575*cos(.5977*x)