A string $3\mathrm{.}50$ m long and fixed at both ends is vibrating in its third harmonic. The maximum displacement of any point on the string is $4\mathrm{.}00$ mm $.$ The speed of transverse waves on this string is $43\mathrm{.}4\frac{m}{s}.$

What are the wavelength $$ and frequency $f$ of this standing wave?

$=$

m

$f=$

Hz

Assume that the standing wave is at its maximum amplitude at time $t=0s.$

What is the wave function $y(x,t)$ for this standing wave, where the position $y$ is in millimeters and the position $x$ is in meters?

$y(x,t)=$

$$ mm

Enter your expression in terms of $x,t,$ and decimal$-$value coefficients with three significant figures.