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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?
phy123/lab_8.1257958206.txt · Last modified: 2009/11/11 11:50 by mdawber
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