The wave function associated with standing waves established in a $5\mathrm{.}00$ m long cord is

y $=0\mathrm{.}00900$ sin$($x$)$cos$(160$t$)$

where x and y are in meters and t is in seconds.

$($a$)$

How many half$-$wavelengths does this pattern exhibit?

half$-$wavelength$($s$)$

$($b$)$

What is the fundamental frequency of vibration of the cord $($in Hz$)?$

Hz

$($c$)$

If the original frequency is held constant and the tension in the cord is increased by a factor of $25,$ how many half$-$wavelengths are present in the new pattern?

half$-$wavelength$($s$)$