Question

A good definition of a “wave” is a disturbance of a continuous medium that propagates with a fixed shape at constant velocity. (Griffiths, 1999, Introduction to Electrodynamics). Another way of saying this is the medium (e.g. a string, water, or air) will only propagate a wave as long as its shape satisfies the wave equation: d^2 f/dx^2 =1/v^2 . d^2 f/dt^2 a) Show explicitly whether the displacement function f(x,t) = A sin(kx) cos(ωt) will be propagated in a medium as a wave or not. (5) b) Do the same for the function f(x,t) = A exp(−b(bx2 + vt)) (5) c) Could a string support a disturbance of the form f(x,t)=Asin(kx)cos(x−ωt) as a wave? Your professor will show you what this looks like in class and you will immediately

Answer 1