Standing Wave

the purpose of this lab is to learn and understand the idea of standing waves driven by an external force, we are going to measure and compare different wavelength and frequency of waves on a single string, but by changing the frequency of the wave we can adjust the pattern that we see

we measured the weight and length of the string to be 1.2g and 131cm

we had two cases for this lab, by changing the amount of tension we give to the string we should be able to change the v and thus the frequency of the string, although whether the length of the wavelength changes we do not know.

      Test 1 with 100g                                                            
nodes          frequency             Wavelength                                      
1                    11 hz                     2.62                                  
2                    25 hz                     1.31
3                    34 hz                     .873
4                    46 hz                     .655                                  
5                    56 hz                     .524    
6                    69 hz                     .436  
7                    77 hz                     .374
8                    93 hz                     .3275            
9                    102 hz                   .291

speed of wave v = sqrt( T/u )
with this graph i gotten the v of the wave to be about 47.82 m./s +_ 2.85 m/s


    Test 2 with 200g
 nodes                 frequency             Wavelength
 1                             16 hz                2.62
 2                             34 hz                1.31
 3                             46 hz                .873
 4                             64 hz                .655
 5                             79 hz                .524
 6                             95 hz                .436
 7                            110 hz               .374
 8                            126 hz               .3275
 9                            144 hz               .291

speed of wave v = sqrt( T/u )
with this graph i gotten the v of the wave to be about 53.82 m./s +_ 3.15 m/s



Ratio of  the frequency

16/11 = 1.45
34/25 = 1.409
46/34  = 1.35
64/46 = 1.39
79/56 = 1.41
95/69 = 1.37
110/77 = 1.42
126/93 = 1.35
144/102 = 1.17


after comparing the ratios of the frequencies we find that it's avg its about 1.35 +_ 0.27, but as we can see all of the data points are pretty close to the avg meaning that the experimental data should be linear as we seen in the groups above

analysis
we can conclude that the frequencies and wavelength is directly proportional to the tension of the string and its mass per unit length thus proving the equations of
                                           v = (frequency)(wavelength) = sqrt(tension)/(mass per unit length) = v