$6.$ Two very long strings are joined at the position $=0$ and placed under a tension of $100$ N$.$ The string at $<0$ has mass density $=0\mathrm{.}5$ kg$/$m while the string at $>0$ has mass density $=1$ kg$/$m$.$ A wave of the form $(,)=$cos$()$ is incident from $<0.$ If the incident angular frequency $$ is $1\mathrm{.}0$ rad$/$s and the incident amplitude $$ is $10$ cm$,$ then the displacement of the particle at $=+1\mathrm{.}0$ m is: A$)()=(8\mathrm{.}3$ cm$)$cos$(0\mathrm{.}63)$ B$)()=(6\mathrm{.}7$ cm$)$cos$(0\mathrm{.}63)$ C$)()=(6\mathrm{.}7$ cm$)$ cos$(0\mathrm{.}10)$ D$)()=(8\mathrm{.}3$m$)$cos$(0\mathrm{.}10)$