Four traveling waves are described by the following equations,where all quantities are measured in SI units and y represents the displacement. I: y = 0.12 cos(3x - 21t)
II: y = 0.15 sin(6x + 42t)
III: y = 0.13 cos(6x + 21t)
IV: y = -0.27 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 given by the equation T = 2π/ω, where ω is the angular frequency. For wave I, ω = 21 rad/s, so T = 2π/21 s ≈ 0.3 s. For wave III, ω = 21 rad/s, so T = 2π/21 s ≈ 0.3 s. For wave II, ω = 42 rad/s, so T = 2π/42 s ≈ 0.15 s. For wave IV, ω = 42 rad/s, so T = 2π/42 s ≈ 0.15 s. Therefore, waves I and III have the same period, and waves II and IV have the same period.

Four Traveling Waves Are Described by the Following Equations,where All