A sinusoidal wave of wavelength 7.5 cm travels 1.2 cm along the +x direction in 0.3 s. At t = 0, a crest P is at x = 0 and the maximum displacement is 2 cm. Which equation correctly represents the wave?
Options

Question

A sinusoidal wave of wavelength 7.5 cm travels 1.2 cm along the +x direction in 0.3 s. At t = 0, a crest P is at x = 0 and the maximum displacement is 2 cm. Which equation correctly represents the wave?

Options

G1 Physics · Accepted Answer

Since a crest is at x=0 when t=0, a cosine form is appropriate: y = A cos(kx - ωt). Amplitude: A = 2 cm. Wave number: k = 2π/λ = 2π/7.5 ≈ 0.83 rad/cm. Wave speed: v = distance/time = 1.2/0.3 = 4 cm/s. Angular frequency: ω = vk = 4×0.83 ≈ 3.35 rad/s. Hence y = 2 cos(0.83x - 3.35t) cm. Correct option: C.