Two waves travel simultaneously through the same medium. The first wave is described by y₁(x,t) = (2.00 cm)cos[kx-ωt] and the second wave by y₂(x,t) = (3.00 cm)sin(kx-ωt). If the resulting superposition can be written as y(x,t) = Ccos(kx-ωt + δ), what is the value of δ? A)0.983 B)1.50 C)0.833 D)0.782 E)0.667

Question

Quizplus · Accepted Answer

The superposition of the two waves can be expressed in the form y(x,t) = Ccos(kx-ωt + δ) using the trigonometric identity for the sum of a cosine and sine function. The phase angle δ is given by δ = arctan(B/A), where A = 2.00 cm and B = 3.00 cm. Thus, δ = arctan(3/2) ≈ 0.983 radians.

Two Waves Travel Simultaneously Through the Same Medium