18.Standing waves are produced by the superoposition of two waves y1=a sin (wt-kx), y2=a sin(wt+kx).The amplitude of a particle at distance x is --------
y1 = a sin (wt - kx)
and y2 = a sin (wt + kx )
y = y1 + y2
y = a [ sin (wt - kx)+ sin (wt+ kx) ]
y = a [sinwt coskx - coswt sinkx + sinwt coskx + coswt sinkx ]
y = 2a sinwt coskx
y = (2a coskx ) sinwt
y = A sinwt
Amplitude of resultant wave (particle) at distance x is (2a coskx )
and y2 = a sin (wt + kx )
y = y1 + y2
y = a [ sin (wt - kx)+ sin (wt+ kx) ]
y = a [sinwt coskx - coswt sinkx + sinwt coskx + coswt sinkx ]
y = 2a sinwt coskx
y = (2a coskx ) sinwt
y = A sinwt
Amplitude of resultant wave (particle) at distance x is (2a coskx )