A transverse wave on a string is described by the wave function y$=$y$0$sin$($kx$+$t$)$y$=$y$0$sin$($kx$+$t$),$ where y$0=0\mathrm{.}103$y$0=0\mathrm{.}103$m$,$ k$=0\mathrm{.}338$k$=0\mathrm{.}338$m$11,$ and $=11\mathrm{.}7$$=11\mathrm{.}7$s$11.$ At time t$=0\mathrm{.}200$t$=0\mathrm{.}200$s and string position x$=1\mathrm{.}6$x$=1\mathrm{.}6$m$,$ determine the following quantities:

$($a$)$

Wavelength.

m $(0\mathrm{.}2$ m$)$

$($b$)$

Wavenumber $($angular$).$

m$11(0\mathrm{.}002$ m$11)$

$($c$)$

Wave frequency $($cyclic$).$

Hz $(0\mathrm{.}02$ Hz$)$

$($d$)$

Wave period.

s $(0\mathrm{.}002$ s$)$

$($e$)$

Wave velocity $($magnitude and sign$).$

m$/$s $(0\mathrm{.}2$ m$/$s$)$

$($f$)$

Transverse string position $($magnitude and sign$).$

m $(0\mathrm{.}002$ m$)$

$($g$)$

Peak transverse string position $($magnitude$).$

m $(0\mathrm{.}002$ m$)$

$($h$)$

Average transverse string position $($magnitude$).$

m $(0\mathrm{.}002$ m$)$

$($i$)$

Transverse string velocity $($magnitude and sign$).$

m$/$s $(0\mathrm{.}02$ m$/$s$)$

$($j$)$

Transverse string acceleration $($magnitude and sign$).$

m$/$s$2(0\mathrm{.}2$ m$/$s$2)$