The displacement of a string carrying a traveling sinusoidal wave is given by At time t = 0 the point at x = 0 has velocity v₀ and displacement y₀. The phase constant $\phi$is given by tan$\phi$=: A) v₀/ $ \omega $y₀ B) $ \omega $y₀/v₀ C) $ \omega $v₀/y₀ D) y₀/ $ \omega $v₀ E) $ \omega $v₀y₀

Question

Quizplus · Accepted Answer

The general form of a traveling sinusoidal wave is given by y(x,t) = A*cos(kx-ωt+φ) where A is the amplitude, k is the wave number, ω is the angular frequency, and φ is the phase constant. At x=0 and t=0, y₀ = A*cos(φ) and v₀ = -A*ω*sin(φ) We can solve for the phase constant φ by taking the tangent of the equation for velocity and dividing by the equation for displacement: tan(φ) = v₀/y₀ Using the relationship between phase constant and angular frequency, φ = -ωt + φ0, we can rearrange the equation to get: tan(φ0) = F1F1F1S1F1F1F10*y₀/v₀ Therefore, the best choice is B.

The Displacement of a String Carrying a Traveling Sinusoidal Wave ϕ\phiϕ

The Displacement of a String Carrying a Traveling Sinusoidal Wave $\phi$