A sinusoidal wave propagates along a string. In figure (a)and (b) 'y' represents displacement of aprticle from the mean position. 'x'& 't' have usual meanings . Find : (a) wavelength, freuency and speed of the wave. (b) maximum velocity and maximum acceleration of the particles. (c) the magnitude of slopes of the string at x=2 at t=4sec.

A sinusoidal wave propagates along a string. In figure (a)and (b) 'y'

1.	A sinusoidal wave propagates along a string. In figure (a)and (b) 'y' represents displacement of aprticle from the mean position. 'x'& 't' have usual meanings . Find : (a) wavelength, freuency and speed of the wave. (b) maximum velocity and maximum acceleration of the particles. (c) the magnitude of slopes of the string at x=2 at t=4sec.
Answer» SOLUTION :`(a)` from `y-x` graph wavelength `=lambda = 6M` from `y-t` graph Time period `=T=4 sec` `rArr `frequency `=f=(1)/(4)=0.25Hz` wave speed `=f lambda=0.25 xx 6 =1.50 m//s` `(b)` maximum `=3 m m xx (pi)/(2) rad //sec = 1.5 pi m m //sec` maximum acceleration `=w^(2) A =(pi^(2))/(4) xx 3m m=0.75 p^(2) mm //sec^(2).` `(c ) k=(2PI)/(lambda)=(pi)/(3) m^(-1)` `rArr w=(2pi)/(T)=(pi)/(2) rad // sec` `y=3 sin ((pi)/(3)xx-(pi)/(2) t+theta_(0))` `y(x=2,t=0)=0` `rArr sin ((2pi)/(3)+theta_(0))=0` `rArr THETA _(0)=-(2pi)/(3) ` or `(pi)/(3)` and `(dely)/(delt)(t=0,x=2) gt 0` `rArr (-3pi)/(2) cos ((pi)/(3) x-(pit)/(2)+theta_(0)) gt 0` `(` For `x=2,t=0)` `rArr cos ((2pi)/(3)+theta_(0)) lt 0` `rArr theta_(0)=(pi)/(3)` `y=(x,t)=3 sin ((pix)/(3)-(pit)/(2)+(pi)/(3))` `rArr `at `x=2 ` and `t=4 sec, (dely)/(delx)=pi`