Answer:
y = 0.010 cos ( 1539.4 t + 0.645)
Explanation:
The general equation for a wave on a string is
y = A sin (kx - wt)
Where k is the wave number
k = 2π /λ
k = 2π / 3 10⁻²
k = 209.4 m⁻¹
The angular velocity is related to the frequency
w = 2π f
w = 2π 245
w = 1539.4 rad / s
The maximum amplitude is
.A = 0.0100 m
The wave equation is
y = 0.01 sin (-209.4 x - 1539.4 t)
The particle that is at each point of this wave performs an oscillatory movement perpendicular to the wave discarded by
y = yo cos (wt + fi)
The angular velocity of the particle is equal to the velocity of the wave
w = 1539.4 rad / s
The breadth of displacement is
y₀ = 0.01 m
With the initial data let's look for the phase
0.008 = 0.01 cos (0+ Ф)
Ф = cos⁻¹ (0.008 / 0.01)
Ф = 0.645 rad
Therefore the equation is
y = 0.010 cos ( 1539.4 t + 0.645)
