18
Guitar Strings SRJC, Engr 45, Fall 2013 By Kyle Cubba Peter de Rutte Xavier Kouoi
Guitar Strings
SRJC, Engr 45, Fall 2013
By Kyle Cubba
Peter de Rutte Xavier Kouoi
Objective
• The purpose of this experiment was to determine the modulus of elasticity for various guitar strings.
Background
• Modulus of Elasticity indicates the behavior of materials that undergo elastic deformation.
• Modulus of elasticity (Young’s modulus) is the ratio of stress over strain.
• Stress is calculated by dividing the force by the cross-sectional area of the string.
• Strain is calculated by dividing the change in length by the initial length.
Callister Materials Science and Engineering An Introduction 8th Edition
Method
Apparatus
• The apparatus uses two collets that hold a thin wire fixed at two places. The collet at the top remains static while the bottom one is free to move downward when weight is added. When weight is applied, the bar presses down on a dial indicator which reads how much the string is stretched.
Calculating Stress
• Measure diameter of string and calculate cross-sectional area.
• F=mg • Calculate stress by dividing
Force by area.
Calculating Strain
• Initial length is the distance between collets
• Any change in length is seen on dial indicator
• Divide change in length by initial length to find strain.
Materials Tested
Nickel-plated Steel Single wire & coiled wire
Bronzed Steel Single wire & coiled wire
Data Mass (kg) Force (N) Delta L (in.) Delta L (m) Stress (N/m^2) Strain
1 9.8 0.02 0.000508 70735530.26 0.000818
2 19.6 0.035 0.000889 141471060.5 0.001432
3 29.4 0.047 0.0011938 212206590.8 0.001922
4 39.2 0.055 0.001397 282942121.1 0.00225
5 49 0.064 0.0016256 353677651.3 0.002618
6 58.8 0.074 0.0018796 424413181.6 0.003027
7 68.6 0.083 0.0021082 495148711.8 0.003395
8 78.4 0.0925 0.0023495 565884242.1 0.003783
9 88.2 0.101 0.0025654 636619772.4 0.004131
10 98 0.108 0.0027432 707355302.6 0.004417
11 107.8 0.118 0.0029972 778090832.9 0.004826
12 117.6 0.126 0.0032004 848826363.2 0.005154
13 127.4 0.134 0.0034036 919561893.4 0.005481
14 137.2 0.143 0.0036322 990297423.7 0.005849
15 147 0.1525 0.0038735 1061032954 0.006238
16 156.8 0.159 0.0040386 1131768484 0.006503
17 166.6 0.166 0.0042164 1202504014 0.00679
17.5 171.5 0.183 0.0046482 1237871780 0.007485
17.7 173.46 0.185 0.004699 1252018886 0.007567
Nickel-plated steel, single-wire:
0
200
400
600
800
1000
1200
1400
0 0.002 0.004 0.006 0.008
Stre
ss (M
Pa/m
^2)
Strain (m/m)
Mass (kg) Force (N) Delta L (in.) Delta L (m) Stress (N/m^2) Strain
1 9.8 0.008 0.000203 21602749 0.000323
2 19.6 0.019 0.000483 43205497 0.000766
2.5 24.5 0.025 0.000635 54006871 0.001008
3 29.4 0.03 0.000762 64808246 0.00121
3.5 34.3 0.0355 0.000902 75609620 0.001431
4 39.2 0.041 0.001041 86410994 0.001653
4.5 44.1 0.0465 0.001181 97212368 0.001875 5 49 0.0525 0.001334 1.08E+08 0.002117
5.5 53.9 0.0572 0.001453 1.19E+08 0.002306 6 58.8 0.062 0.001575 1.3E+08 0.0025
6.5 63.7 0.0675 0.001715 1.4E+08 0.002721 7 68.6 0.073 0.001854 1.51E+08 0.002943
7.5 73.5 0.0785 0.001994 1.62E+08 0.003165 8 78.4 0.085 0.002159 1.73E+08 0.003427
8.5 83.3 0.0905 0.002299 1.84E+08 0.003649 9 88.2 0.096 0.002438 1.94E+08 0.00387
9.5 93.1 0.101 0.002565 2.05E+08 0.004072 10 98 0.107 0.002718 2.16E+08 0.004314
10.5 102.9 0.113 0.00287 2.27E+08 0.004556 11 107.8 0.119 0.003023 2.38E+08 0.004798
11.5 112.7 0.1235 0.003137 2.48E+08 0.004979 12 117.6 0.13 0.003302 2.59E+08 0.005241
12.5 122.5 0.135 0.003429 2.7E+08 0.005443 13 127.4 0.141 0.003581 2.81E+08 0.005685
13.5 132.3 0.146 0.003708 2.92E+08 0.005886 14 137.2 0.152 0.003861 3.02E+08 0.006128
14.5 142.1 0.157 0.003988 3.13E+08 0.00633 15 147 0.164 0.004166 3.24E+08 0.006612
15.5 151.9 0.17 0.004318 3.35E+08 0.006854 16 156.8 0.176 0.00447 3.46E+08 0.007096
16.5 161.7 0.1815 0.00461 3.56E+08 0.007318 17 166.6 0.189 0.004801 3.67E+08 0.00762
17.5 171.5 0.194 0.004928 3.78E+08 0.007822
Bronzed-steel, coiled-wire
0
50
100
150
200
250
300
350
400
0 0.002 0.004 0.006 0.008 0.01
Stre
ss (M
Pa/m
^2)
Strain (m/m)
Mass (kg) Force (N) Delta L (in.) Delta L (m) Stress (N/m^2) Strain
1 9.8 0.0055 0.0001397 26208249.4 0.000259
2 19.6 0.015 0.000381 52416498.8 0.000706
3 29.4 0.023 0.0005842 78624748.19 0.001082
4 39.2 0.032 0.0008128 104832997.6 0.001505
5 49 0.0405 0.0010287 131041247 0.001905
6 58.8 0.049 0.0012446 157249496.4 0.002305
7 68.6 0.0575 0.0014605 183457745.8 0.002705
8 78.4 0.066 0.0016764 209665995.2 0.003104
9 88.2 0.075 0.001905 235874244.6 0.003528
10 98 0.083 0.0021082 262082494 0.003904
11 107.8 0.092 0.0023368 288290743.4 0.004327
12 117.6 0.101 0.0025654 314498992.8 0.004751
13 127.4 0.1095 0.0027813 340707242.2 0.005151
14 137.2 0.118 0.0029972 366915491.6 0.00555
15 147 0.127 0.0032258 393123741 0.005974
16 156.8 0.135 0.003429 419331990.4 0.00635
17.5 171.5 0.147 0.0037338 458644364.5 0.006914
18.5 181.3 0.158 0.0040132 484852613.9 0.007432
19.5 191.1 0.164 0.0041656 511060863.3 0.007714
20.5 200.9 0.174 0.0044196 537269112.7 0.008184
Nickel-plated steel, coiled-wire
0
100
200
300
400
500
600
0 0.002 0.004 0.006 0.008 0.01
Stre
ss (M
Pa/m
^2)
Strain (m/m)
Mass (kg) Force (N) Delta L (in.) Delta L (m) Stress (N/m^2) Strain
0.5 4.9 0.016 0.0004064 48139458.1 0.000635
1 9.8 0.025 0.000635 96278916.19 0.000992188
1.5 14.7 0.033 0.0008382 144418374.3 0.001309688
2 19.6 0.0395 0.0010033 192557832.4 0.001567656
2.5 24.5 0.046 0.0011684 240697290.5 0.001825625
3 29.4 0.051 0.0012954 288836748.6 0.002024063
3.5 34.3 0.0585 0.0014859 336976206.7 0.002321719
4 39.2 0.065 0.001651 385115664.8 0.002579688
4.5 44.1 0.072 0.0018288 433255122.9 0.0028575
5 49 0.078 0.0019812 481394581 0.003095625
5.5 53.9 0.084 0.0021336 529534039.1 0.00333375
6 58.8 0.0915 0.0023241 577673497.1 0.003631406
6.5 63.7 0.0995 0.0025273 625812955.2 0.003948906
7 68.6 0.1055 0.0026797 673952413.3 0.004187031
7.5 73.5 0.111 0.0028194 722091871.4 0.004405313
8 78.4 0.118 0.0029972 770231329.5 0.004683125
8.5 83.3 0.125 0.003175 818370787.6 0.004960938
9 88.2 0.131 0.0033274 866510245.7 0.005199063
9.5 93.1 0.1385 0.0035179 914649703.8 0.005496719
10 98 0.144 0.0036576 962789161.9 0.005715
10.5 102.9 0.152 0.0038608 1010928620 0.0060325
11 107.8 0.158 0.0040132 1059068078 0.006270625
11.5 112.7 0.167 0.0042418 1107207536 0.006627813
12 117.6 0.1725 0.0043815 1155346994 0.006846094
12.5 122.5 0.18 0.004572 1203486452 0.00714375
13 127.4 0.187 0.0047498 1251625910 0.007421563
13.5 132.3 0.194 0.0049276 1299765369 0.007699375
14 137.2 0.201 0.0051054 1347904827 0.007977188
14.5 142.1 0.208 0.0052832 1396044285 0.008255
15 147 0.214 0.0054356 1444183743 0.008493125
15.5 151.9 0.221 0.0056134 1492323201 0.008770938
16 156.8 0.229 0.0058166 1540462659 0.009088438
16.5 161.7 0.236 0.0059944 1588602117 0.00936625
17 166.6 0.244 0.0061976 1636741575 0.00968375
17.5 171.5 0.254 0.0064516 1684881033 0.010080625
18 176.4 0.2615 0.0066421 1733020491 0.010378281
18.5 181.3 0.268 0.0068072 1781159950 0.01063625
19 186.2 0.276 0.0070104 1829299408 0.01095375
19.5 191.1 0.284 0.0072136 1877438866 0.01127125
20.5 200.9 0.307 0.0077978 1973717782 0.012184063
Bronzed-steel, Single-wire
0
500
1000
1500
2000
2500
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014
Stre
ss (M
Pa/m
^2)
Strain (m/m)
0
500
1000
1500
2000
0 0.002 0.004 0.006 0.008 0.01 0.012
Stre
ss (M
Pa/m
^2)
Strain (m/m)
Stress-Strain Graphs
Bronzed-Steel single wire
Ni-Steel Coiled
Bronzed-Steel coiled
Ni-Steel single wire
Results String Young’s Modulus (GPa)
Single-wire Ni-steel 188
Single-wire Bronzed-steel 174
Coiled wire Ni-steel 64*
Coiled wire Bronzed-steel 48*
1045 Steel (for comparison) 200 (from previous lab)
*These values are not necessarily indicative of the materials’ elasticity because of coiled composition.
Conclusions • The single wires held a deceptively large
amount of weight. • Coiled wires stretched more because of their
spring-like structure, thus the coiled wires’ measured modulus of elasticity is smaller than that of a single wire.
• Coiled structure for larger strings allows for pliability and easy playing for musicians.
Wyatt, Rupert, dir. Rise of the Planet of the Apes. 2011. DVD.
Alone… weak. Together Strong.
Kyle Cubba
Xavier Kouoi
Peter de Rutte
