A transverse wave on a string is described by the following wave function.

y $=$

$0\mathrm{.}095$ sin$$

$9$

x $+3$t

where x and y are in meters and t is in seconds.

$($a$)$ Determine the transverse speed at t $=0\mathrm{.}160$ s for an element of the string located at x $=1\mathrm{.}80$ m$.$

m$/$s

$($b$)$ Determine the transverse acceleration at t $=0\mathrm{.}160$ s for an element of the string located at x $=1\mathrm{.}80$ m$.$

m$/$s$2$

$($c$)$ What is the wavelength of this wave?

m

$($d$)$ What is the period of this wave?

s

$($e$)$ What is the speed of propagation of this wave?

m$/$s