2. Consider a very long string held taut by two students, one on each end. Student A oscillates the end of the string producing a wave modeled with the wave function Y₁(x,t) = a sin (kx-cot) and student B oscillates the string producing at twice the frequency, moving in the opposite direction. Both waves move at the same speed v=. The two waves interfere to form a resulting wave whose wave function is Y(x,t) = Y₁(x,t) + Y₂(x,t). Find the velocity of the resulting wave using the linear wave equation d²Y (x,t) 1 d²Y(x,t) dx² v² dt²

2. Consider a very long string held taut by two students, one on each end. Student A oscillates the end of the string producing a wave modeled with the wave function Y₁(x,t) = a sin (kx-cot) and student B oscillates the string producing at twice the frequency, moving in the opposite direction. Both waves move at the same speed v=. The two waves interfere to form a resulting wave whose wave function is Y(x,t) = Y₁(x,t) + Y₂(x,t). Find the velocity of the resulting wave using the linear wave equation d²Y (x,t) 1 d²Y(x,t) dx² v² dt²