Answer
$x = 0.40~m$
Work Step by Step
$y(x,t) = 0.040~sin(5\pi x)~cos(40 \pi t)$
We can find the values of $x$, where $x \geq 0,$ such that $y = 0$ for all values of $t$:
$y(x,t) = 0.040~sin(5\pi x)~cos(40 \pi t) = 0$
$sin(5\pi x) = 0$
$5\pi x = 0, \pi, 2\pi, 3\pi, ...$
$x = 0, 0.20~m, 0.40~m, 0.60~m, ...$
The location of the node with the third smallest value of $x$ is $~~x = 0.40~m$
