P$3.$ Using the blue wire and a fixed mass of $500$ g $($i$.$e$.450$ g added to the $50-g$ weight hanger$),$ find the frequencies corresponding to $n=1,2,3,4,5,$ and $6$ half$-$wavelengths $("$loops$"$ or anti$-$nodes$).$ Keep the amplitude low $($within limits; the lower the amplitude, the more precise the frequency$).$ You should barely see the tip of the wave generator moving up and down. You may feel it with your finger. Try to obtain the two$-$anti$-$node mode first, then bring the frequency down to half that value and look for the frequency that produces the $n=1($one loop$)$ pattern $($finding this mode may prove to

$8$

be difficult$).$ After that, perform the same for higher values of $n($i$.$e$.$ higher numbers of "loops"$).$

P$3.$ Wire Number $1($The Blue Wire$)$

Total mass $($attached plus hanger$)=500g$

$=7\mathrm{.}440glm,L=57\mathrm{.}25cm$

average $v_{\text{p}\text{a}\text{t}\text{e}\text{m}}=13\mathrm{.}614\frac{m}{sec}$

$v_{\text{c}\text{a}\text{l}\text{c}\text{u}\text{l}\text{a}\text{t}\text{e}\text{d}}=\sqrt[\phantom{2}]{m\frac{g}{}}=25\mathrm{.}66324514$

P$4.$ Wire Number $2($The Yellow Wire$)$ Total mass $($attached plus hanger$)=500g$

$=3\mathrm{.}080\frac{g}{m},L=145\mathrm{.}5cm$

average $v_{\text{p}\text{a}\text{t}\text{t}\text{e}\text{r}\text{n}}=20\mathrm{.}5353\frac{m}{sec}$

$v_{\text{c}\text{a}\text{l}\text{c}\text{u}\text{l}\text{a}\text{t}\text{e}\text{d}}=\sqrt[\phantom{2}]{m\frac{g}{}}=39\mathrm{.}8862017S$

P$5.$ Wire Number $2($Yellow Wire$)$ with Varying Hanging Mass