Question

A wave propagates on a strong in the positive x-direction at a velocity v. the shape of the string at t = t' is given by g(x,t') = Asin(x/a) . write the wave equation for a general time t. ​

Answer 1

Solution :- At t = t' g ( x, t')= Asin(x/a) ______(1)

For a wave traveling in the positive x-direction

the general equation is given by

y = f [x/a- t'/T]

Putting T= -t' and comparing with equation (1) , we get

=> g(x,0)=Asin(x/a+ t'/T)

=> g(x,t) = Asin(x/a+t'/T- t/T)

As , t = a/v

=> y = Asin{x/a+ t'/(a/v)- t/(a/v)

=>Asin{x+ v(t'-t)/a}

=> y = Asin{x- v(t-t')/a

is the required equation.