A sinusoidal wave on a string is caused by shaking the end of the string up and down with a frequency of $3$ Hz$,$ and a maximum displacement from the center of $8$ cm$.$ The mass per unit length of this string is $12\mathrm{.}0$ g$/$m$,$ and it is stretched to a tension of $10$ N$.$ a$.$ Determine the speed of the wave. b$.$ Determine the wavelength. c$.$ Determine the wave number. d$.$ Determine the angular frequency. e$.$ Write down the displacement equation as a function of x and t$,$ using the numbers above. f$.$ Determine the power transmitted by the wave.