Answer:
T = 3.14 10⁻² s
Explanation:
The general equation for a traveling transverse wave is
y = A sin (k x - wt +Ф)
where w is the angular velocity that is related to the period and Ф is the phase of the oscillation
w = 2π / T (1)
In this case they indicate that the expression of the wave
y = 0.003 cos (20 x + 200t)
if we use the relationship of the double angles
a = kx - wt
b = Ф
sin (a + b) = sin a cos b + sin b cos a
for the case Ф = 90 we have
sin (a + b) = cos b
we substitute
y = A cos (kx -wt)
with an initial phase of fi = 90º
if we compare the terms of the two expressions
A = 0.003 m
k = 20 m⁻¹
w = -200 rad/s
the negative sign indicates that the wave goes to the left
if we clear from equation 1
T = 2π / w
T = 2π / 200
T = 3.14 10⁻² s
