Four waves are described by the following expressions, where distances are measured in meters and times in seconds. I y = 0.12 cos(3x - 21t)
II y = 0.15 sin(6x + 42t)
III y = 0.13 cos(6x + 21t)
IV y = -0.23 sin(3x - 42t)
Which of these waves travel in the +x direction?
A) I and II
B) I and III
C) II and IV
D) I and IV
E) II and III

Question

Quizplus · Accepted Answer

To determine the direction of wave motion, we need to look at the expression inside the parentheses for each wave. If the coefficient of x is positive, the wave is moving in the +x direction. If the coefficient is negative, the wave is moving in the -x direction. 
- Wave I: 3x - 21t has a positive coefficient for x, so it's moving in the +x direction. 
- Wave II: 6x + 42t also has a positive coefficient for x, so it's moving in the +x direction. 
- Wave III: 6x + 21t has a positive coefficient for x, so it's moving in the +x direction. 
- Wave IV: 3x - 42t has a negative coefficient for x, so it's moving in the -x direction.

Therefore, the only waves that travel in the +x direction are Waves I and IV, making choice D the correct answer.

Four Waves Are Described by the Following Expressions, Where Distances