A $38\mathrm{.}0-$gram, $7\mathrm{.}00-$meter wire is subject to a tension force of $44\mathrm{.}0$ N$,$ with both ends fixed. Adopt a coordinate system in which the wire lies along the x$-$axis, with one end at

x $=0$

and the other at x $=7\mathrm{.}00$ m$.$

$($a$)$

Determine the positions $($x$-$values$)$ of the nodes and antinodes when the wire is exhibiting the third harmonic. $($Enter your answers, in m$,$ from smallest to largest.$)$

$1$st nodex$=$ m$1$st antinodex$=$

When a wire with fixed ends vibrates in its third harmonic, how many nodes are found along the wire's length? How many antinodes? How many node$-$antinode$-$node $($N$-$A$-$N$)$ segments lie between the wire's ends? Use this reasoning, and the wire's length L$,$ to calculate the separation between adjacent nodes. Then, to calculate the antinode positions, note that each antinode is halfway between the nodes to either side. m$2$nd nodex$=$ m$2$nd antinodex$=$

When a wire with fixed ends vibrates in its third harmonic, how many nodes are found along the wire's length? How many antinodes? How many node$-$antinode$-$node $($N$-$A$-$N$)$ segments lie between the wire's ends? Use this reasoning, and the wire's length L$,$ to calculate the separation between adjacent nodes. Then, to calculate the antinode positions, note that each antinode is halfway between the nodes to either side. m$3$rd nodex$=$

When a wire with fixed ends vibrates in its third harmonic, how many nodes are found along the wire's length? How many antinodes? How many node$-$antinode$-$node $($N$-$A$-$N$)$ segments lie between the wire's ends? Use this reasoning, and the wire's length L$,$ to calculate the separation between adjacent nodes. Then, to calculate the antinode positions, note that each antinode is halfway between the nodes to either side. m$3$rd antinodex$=$

When a wire with fixed ends vibrates in its third harmonic, how many nodes are found along the wire's length? How many antinodes? How many node$-$antinode$-$node $($N$-$A$-$N$)$ segments lie between the wire's ends? Use this reasoning, and the wire's length L$,$ to calculate the separation between adjacent nodes. Then, to calculate the antinode positions, note that each antinode is halfway between the nodes to either side. m$4$th nodex$=$