Suppose a string is stretched horizontally and then plucked. Let u(x, t) rep- resent the vertical...

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Suppose a string is stretched horizontally and then plucked. Let u(x, t) rep- resent the vertical displacement of the string at position x and time t. (a) Give physical and/or graphical interpretations of the partial derivatives u(x,t) and u(x, t). Give graphical interpretations of ux(x, t) and uxx(x, t). (b) Suppose u(x,t) satisfies the wave equation u = a u xx. What is an interpretation of the wave equation in terms of acceleration and con- cavity? Suppose a string is stretched horizontally and then plucked. Let u(x, t) rep- resent the vertical displacement of the string at position x and time t. (a) Give physical and/or graphical interpretations of the partial derivatives u(x,t) and u(x, t). Give graphical interpretations of ux(x, t) and uxx(x, t). (b) Suppose u(x,t) satisfies the wave equation u = a u xx. What is an interpretation of the wave equation in terms of acceleration and con- cavity?