A wave is described by y(x,t)= 0.1 sin(3x - 10t), where x is in meters, y is in centimeters and t is in seconds.At time t = 0, the point at x = 0 has a vertical displacement y = 0.0 cm.When is its displacement equal to 0.1 cm?
A)0.16 s
B)0.47 s
C)2.5 s
D)7.5 s
E)10 s

Question

Quizplus · Accepted Answer

Setting the equation equal to 0.1 cm and solving for t, we get:

0.1 = 0.1 sin(3x - 10t)
1 = sin(3x - 10t)
sin⁻¹(1) = 3x - 10t
90° = 3x - 10t
t = (3/10)x - 9°

At x = 0, the point in question is located. So,

t = (3/10)×0 - 9°
t = 0 + 9°
t = 9/90 s
t = 0.1 s

Therefore, the displacement of the point at x = 0 is equal to 0.1 cm at time t = 0.1 s, which is option B.

A Wave Is Described by Y(x,t)= 0