$(10$pts$)$ A transverse wave on a string is described by the following wave function:

$y=0\mathrm{.}085sin(\frac{}{11}x+3t)$

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

a$)$ Determine the transverse speed at $t=0\mathrm{.}280$ s for an element of the string located at $x=1\mathrm{.}50m.$

b$)$ Determine the transverse acceleration at $t=0\mathrm{.}280s$ for an element of the string located at $x=1\mathrm{.}50m.$

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

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

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

Make sure and show all your work $-$ draw diagrams if you want, show equations, discuss principles, and so forth, in your answers.