$4.$ A continuous sinusoidal longitudinal wave propagates along a very long coiled spring, generated by an attached oscillating source. The wave travels in the negative direction of the x$-$axis. The source frequency is $25$ Hz$,$ at any instant the distance between successive points of maximum expansion in the spring is $24$cm; the maximum longitudinal displacement of a spring particle is $0\mathrm{.}30$ cm; and theparticle at x $=0$ has zero displacement at time t $=0.($a$)$ Calculate the wave speed$\mathrm{.}55=254$z$.($b$)$ Write down the expression for this sinusoidal wave. $(20$ points$)$