A wave propagates on a string in the positive x-direction at a velocity u. The shape of the string at t=t_0is given by g(x, t_0)= A sin(x /a) . Write the wave equation for a general time t.

A wave propagates on a string in the positive x-direction at a velocit

1.	A wave propagates on a string in the positive x-direction at a velocity u. The shape of the string at t=t_0is given by g(x, t_0)= A sin(x /a) . Write the wave equation for a general time t.
Answer» Solution :At `t=t_0, {t(x,t_0)}=Asin(x/a)` For a WAVE travelling in the positive x-direction the general EQUATIONN is given by `y=Asin(x/a-t/T)` Putting t=-t and comparing with equation 1 we get `RARR G(x,0)=Asin{(x/a)+(t_0/t)}` `rarr g(x,t)=Asin[{(x/a)+t_0/T}-(t/T)]` As T=a/v` a=wave LENGTH v=speed of the wave `rarr y=A sin[(x/y)+t_0/((a/v))-t/((a/v))` `rarr y=Asin(x+v(t_0-t))/a`