# Differences

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phy123:lab_8 [2009/11/11 11:50]
mdawber
phy123:lab_8 [2009/11/17 17:48] (current)
mdawber
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The purpose of this lab is to study standing waves on a vibrating string. The purpose of this lab is to study standing waves on a vibrating string.
+
+[[http://​www.ic.sunysb.edu/​Class/​phy122ps/​labs/​dokuwiki/​pdfs/​lab8worksheet.pdf|Important! You need to print out the 2 page worksheet you find by clicking on this link and bring it with you to your lab session.]]
+
+If you need the .pdf version of these instructions you can get them [[http://​www.ic.sunysb.edu/​Class/​phy122ps/​labs/​dokuwiki/​pdfs/​phy123lab8.pdf|here]].
+
+===== Video =====
+
+<​flashplayer width=640 height=480>​file=http://​www.ic.sunysb.edu/​Class/​phy122ps/​labs/​phy121vid/​phy123lab8.flv</​flashplayer>​
+

===== Equipment ===== ===== Equipment =====
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{{lab8fig2.jpg?​600}} {{lab8fig2.jpg?​600}}
+Fig 2.

The equation for the velocity of a travelling wave on a string is  The equation for the velocity of a travelling wave on a string is
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</​WRAP>​ </​WRAP>​
<WRAP column 45%> <WRAP column 45%>
-$\Large \frac{1}{2}\frac{\Delta v}{v}=\frac{\Delta \mu}{\mu}$+$\Large \frac{\Delta v}{v}=\frac{1}{2}\frac{\Delta \mu}{\mu}$
</​WRAP>​ </​WRAP>​
<WRAP column 10%> <WRAP column 10%>
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By combining equations (8.1), (8.3) and (8.6) you can obtain an equation for the frequency $f_{3}$ as a function of the mass M that has is hung from it. By combining equations (8.1), (8.3) and (8.6) you can obtain an equation for the frequency $f_{3}$ as a function of the mass M that has is hung from it.

+<WRAP column 35%>\\
+</​WRAP>​
+<WRAP column 45%>
+$\Large f_{3}^2=\frac{3^2}{(2L)^2}\frac{g}{\mu}M$
+</​WRAP>​
+<WRAP column 10%>
+(8.7)
+</​WRAP>​
+\\
+\\
+
+Replace the “rubbery” string with the thick white string. The string does not stretch noticeably when put under tension, thus having a fixed linear mass density for various tensions. Determine its linear mass density $\mu$ as you did for the rubber band in Part I.
+
+Vary the tension T by suspending masses M = 50, 100, 150, 200 grams. Measure the frequencies $f_{3}$ for the standing wave with 3 half – waves for each mass M and enter them with their squares (ie as $f_{3}^2$) in the table on your worksheet.
+
+Graph $f_{3}^2$ vs M using the tool below (no errors). You should check the box that asks if you the fit goes through (0,​0). ​
+
+<​html>​
+<form method="​post"​ action="​http://​mini.physics.sunysb.edu/​~mdawber/​plot/​lab6plot.php"​ target="​_blank">​
+x axis label (include units): <input type="​text"​ name="​xaxis"​ size="​60"/><​br>​
+y axis label (include units): <input type="​text"​ name="​yaxis"​ size="​60"/><​br>​
+Check this box if the fit should go through (0,​0). ​ <input type="​checkbox"​ name="​zero"​ value="​y"​ /><​br>​
+(Don't include (0,0) in your list of points below, it will mess up the fit.)<​br>​
+What kind of errors are you entering below?<​SELECT name="​errortype">​
+<OPTION value="​none">​None</​OPTION>​
+<OPTION value="​x">​Errors in x</​OPTION>​
+<OPTION value="​y">​Errors in y</​OPTION>​
+<OPTION value="​xy">​Errors in x and y</​OPTION>​
+</​SELECT>​
+<br>
+
+x1: <input type="​text"​ name="​x1"​ size="​10"/>​+/​-<​input type="​text"​ name="​dx1"​ size="​10"/>&​nbsp;&​nbsp;&​nbsp;​ y1:  <input type="​text"​ name="​y1"​ size="​10"/>​+/​-<​input type="​text"​ name="​dy1"​ size="​10"/><​br/>​
+x2: <input type="​text"​ name="​x2"​ size="​10"/>​+/​-<​input type="​text"​ name="​dx2"​ size="​10"/>&​nbsp;&​nbsp;&​nbsp;​ y2:  <input type="​text"​ name="​y2"​ size="​10"/>​+/​-<​input type="​text"​ name="​dy2"​ size="​10"/><​br/>​
+x3: <input type="​text"​ name="​x3"​ size="​10"/>​+/​-<​input type="​text"​ name="​dx3"​ size="​10"/>&​nbsp;&​nbsp;&​nbsp;​ y3:  <input type="​text"​ name="​y3"​ size="​10"/>​+/​-<​input type="​text"​ name="​dy3"​ size="​10"/><​br/>​
+x4: <input type="​text"​ name="​x4"​ size="​10"/>​+/​-<​input type="​text"​ name="​dx4"​ size="​10"/>&​nbsp;&​nbsp;&​nbsp;​ y4:  <input type="​text"​ name="​y4"​ size="​10"/>​+/​-<​input type="​text"​ name="​dy4"​ size="​10"/><​br/>​
+x5: <input type="​text"​ name="​x5"​ size="​10"/>​+/​-<​input type="​text"​ name="​dx5"​ size="​10"/>&​nbsp;&​nbsp;&​nbsp;​ y5:  <input type="​text"​ name="​y5"​ size="​10"/>​+/​-<​input type="​text"​ name="​dy5"​ size="​10"/><​br/>​
+x6: <input type="​text"​ name="​x6"​ size="​10"/>​+/​-<​input type="​text"​ name="​dx6"​ size="​10"/>&​nbsp;&​nbsp;&​nbsp;​ y6:  <input type="​text"​ name="​y6"​ size="​10"/>​+/​-<​input type="​text"​ name="​dy6"​ size="​10"/><​br/>​
+x7: <input type="​text"​ name="​x7"​ size="​10"/>​+/​-<​input type="​text"​ name="​dx7"​ size="​10"/>&​nbsp;&​nbsp;&​nbsp;​ y7:  <input type="​text"​ name="​y7"​ size="​10"/>​+/​-<​input type="​text"​ name="​dy7"​ size="​10"/><​br/>​
+x8: <input type="​text"​ name="​x8"​ size="​10"/>​+/​-<​input type="​text"​ name="​dx8"​ size="​10"/>&​nbsp;&​nbsp;&​nbsp;​ y8:  <input type="​text"​ name="​y8"​ size="​10"/>​+/​-<​input type="​text"​ name="​dy8"​ size="​10"/><​br/>​
+x9: <input type="​text"​ name="​x9"​ size="​10"/>​+/​-<​input type="​text"​ name="​dx9"​ size="​10"/>&​nbsp;&​nbsp;&​nbsp;​ y9:  <input type="​text"​ name="​y9"​ size="​10"/>​+/​-<​input type="​text"​ name="​dy9"​ size="​10"/><​br/>​
+<input type="​submit"​ value="​submit"​ name="​submit"​ />
+</​form>​
+</​html>​
+\\
+
+Write down the slope of the graph k and it's error. Use this to calculate g the acceleration due to gravity ( From equation (8.7), $k=\frac{3^2}{(2L)^2}\frac{g}{\mu}$ ). To calculate the error in your measurement of g we neglect the error in L and and use the fact that the relative error in g will be due to the relative error in the slope, $\frac{\Delta k}{k}$, and the relative error in $\mu$, $\frac{\Delta \mu}{\mu}$ and from equation (1.7) of Lab 1 will be $\frac{\Delta g}{g}=\sqrt{(\frac{\Delta k}{k})^2+(\frac{\Delta \mu}{\mu})^2}$.

+Once you have your value for g and it's error compare it to the established value. Is it consistent with that? 