Four waves are described by the following equations,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 have the same period?
A)I and III,and also II and IV
B)I and IV,and also II and III
C)I and II,and also III and IV
D)All of them have the same period.
E)They all have different periods.

Question

Quizplus · Accepted Answer

The period of a wave is determined by the coefficient of $t$ in the argument of the sine or cosine function, which is related to the angular frequency $\omega$. Waves I and III have the same absolute value for the coefficient of $t$ (21), indicating they have the same period. Similarly, waves II and IV have the same absolute value for the coefficient of $t$ (42), indicating they also share the same period.

Four Waves Are Described by the Following Equations,where Distances Are