$($cbOWS$,$ iL$)$ A vibrating string $50\mathrm{.}0$ cm long is under a tension of $1\mathrm{.}25$ N $.$ The results from five successive stroboscopic pictures are shown in the figure. The strobe rate is set at $5000$ flashes per minute. Observations reveal that the maximum displacement of the standing wave occurred at flashes $1$ and $5$ with no other maxima in between. $($a$)($cbUS$,$ cG$)$ Find the period, frequency, and wavelength for the traveling waves on this string. $($b$)($cE$)$ What is the speed of the traveling waves on the string? $($c$)($cE$)$ What is the mass of this string? $($bonus$)$ How fast is point $P$ moving when the string is in $($i$)$ position $1$ and $($ii$)$ position $3?$