Word Count : 355

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To find the displacement \( y(x, t) \) of the string, we need to solve the one-dimensional wave equation with the given initial conditions. The wave equation for a string is: \[ \frac{\partial^2 y}{\partial t^2} = c^2 \frac{\partial^2 y}{\partial x^2} \] where \( c \) is the wave speed, determined by the tension and mass per unit length of the string. ### Boundary Conditions: 1. Fixed ends: \( y(0, t) = 0 \) and \( y(l, t) = 0 \) for all \( t \). ### Initial Conditions: _______ ________ _____ _____ ___ ________ ________.
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