The figure is a snapshot of a vibrating string at t = 0. Particle P is moving upward with speed 20π cm s⁻¹ and the string tangent at P makes 6° with the x-axis. (a) Find the wave direction. (b) Find the wave equation. (c) Find the total energy carried per cycle for μ = 50 g m⁻¹.

Question

G1 Physics · Accepted Answer

Step 1: Compare with y = A sin(ωt ± kx + φ): f = ω/(2π), λ = 2π/k and wave speed v = ω/k. Step 2: The sign of kx fixes the propagation direction; particle motion follows ∂y/∂t. Step 3: Apply these to the given coefficients. Final: C: (a) -x direction; (b) y = 4 × 10⁻³ sin[100π(3t + 0.5x + 1/400)] m; (c) 144π² × 10⁻⁵ J.