Answer to Question #86239 in Field Theory for Ajay

Question #86239
Obtain the value of the constant c for which the function u(x,t) = cosαcxsinαt is a
solution of the wave equation :
d^2u/dt^2=c^2(d^2u/dx^2)
1
Expert's answer
2019-03-15T12:38:10-0400
d2u/dt2=α2cosαcxsinαtd^2 u/dt^2= - α^2 cosαcxsinαt

d2u/dx2=α2c2cosαcxsinαtd^2u/dx^2=-α^2c^2cosαcxsinαt

Thus,


α2=c2(α2c2)    c4=1-α^2=c^2(-α^2c^2)\implies c^4=1

c=+1 or c=-1


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