Two plane progressive waves travelling on a string are $$y_1=2.5\times10^{-3}\sin(30x-420t)$$ and $$y_2=2.5\times10^{-3}\sin(30x+420t)$$. superimpose to produce a standing wave.The variables $$x$$ and $$y$$ are in metre and $$t$$ is in second. Then

A

the equation of resultant standing wave is $$y=5\times10^{-3}\cos(30x)\sin(420t)$$

B

the equation of resultant standing wave is $$y=2.5\times10^{-3}\sin(30x)\cos(420t)$$

C

the antinode closest to $$x=0.25\,\text{m}$$ is at $$x=0.262\,\text{m}$$

D

the amplitude of oscillation of particle at $$x=0.17\,\text{m}$$ is $$4.63\,\text{mm}$$