$(16\mathrm{.}1\mathrm{.}20)$ A tube of air of cross section A lies along the $+$x direction, with one end at x $=0.$ A speaker located at x $=0$ vibrates, its displacement relative to its resting position given as a function of time by $()=$ ut s t max cos$()$ where smax $=2\mathrm{.}010-7$m and $=1200$s$-1.$ The temperature is $300$K and the density of air is $1\mathrm{.}16$ kg$/$m$3.($a$)$ What is the frequency of the sound generated by the speaker? $($b$)$ Find the wavefunction s$($x$,$t$)$ which describes the displacement of air in the tube as a function of both position and time. $($c$)$ Find the wavefunctions for pressure and density, P$($x$,$t$),$ and $($x$,$t$).($d$)$ What is the sound level of this wave? Give an example of a real$-$life sound about as loud as this.