A string, fixed on both ends has a linear mass density $0\mathrm{.}00028$ Kg$/$m and length $3\mathrm{.}64$m while initially under tension of $20\mathrm{.}16$N $($a$)$ Determine the speed of waves in the string. $($b$)$ At what frequency would exactly $3$ wavelengths fit on the string? $($c$)$ The tension is now adjusted so that the waves of wavelength $12\mathrm{.}61$cm have a frequency of $65\mathrm{.}97$Hz$.$ What is that tension? $($d$)$ What would now be the frequency of waves that fulfill the condition in part $($b$)?$