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

Oscillating Spring Lab

the purpose of this lab was to show the relationship between the period of the wavelength and the period and thus the frequency.

we used a meter stick to measure the length of the wave and made one wave, meaning we would have to take 2L to get the fun wave length 

we took 4 sets of data each has five points

                                                             wavelength
3m                                    4m                                                 4.6m                              3m
                                                            time (10 oscillations)      

6.01                               8.09                                              9.53                               10.19
6.18                               7.88                                              9.59                                9.96
6.38                               7.86                                              9.45                                9.43
6.03                               7.88                                              9.42                               10.02
6.22                               7.80                                              9.52                               10.05

from these time we can find the period of the oscillating wave
3m             .616s
4m             .7912s
4.6m          .949s
6m             .9935s

analysis
from this we can conclude that the longer wave length well indeed give you a longer period, meaning the frequency of your wave would inversely proportional to the wavelength.
from this lab experiment we have essentially proven the equation
                                                               v=f lamda

Fluid Dynamics

the purpose of this lab is to determine the affects of gravity on fluids using pressure.

the idea of this lab is to use a bucket with a small hole drilled on to the bottom of the bucket, filling it up with water and timing how long the it takes for the water to flow out.

we calculated the bucket to be 11 cm the amount of water that we are experimenting with is about 500 mL with the bucket filled to about 5L

we did some calculations and gotten 6 trials of data

1. 20.33       3. 19.87       5. 20.89
2. 19.74       4. 20.3         6. 20.21

the time difference between these data points seems to be right around 20 s i got the average of the data to be about 20.22+_.369 getting the uncertainty from the rms difference between the average and the data points.

to get the theoretical time it takes for our experiment 

gotten the volume to be about 5*10^-4 m^3

Area 3.167^-5 m^2

g = 9.8 m/s^2

height of the water to about 11cm

using the equation given to me t_theoretical = V/A(2gh)^1/2

i gotten the theoretical time to be about 18.189 and 22.25 to be the min and max of the uncertainties.

which is about 10% error, which is pretty close.

using an error equation 

                                               (t_actual -t_theoretical) /t_actual

analysis
     from this experiment, we can concluded that that knowing the pressure we can find the speed of the water flowing through the bottom of the bucket. if we know the height of the water, and how much water is in the cup after, as well as the time it took.

Fluid Statics Lab

the purpose of this lab was to see the different types of ways that one can measure buoyant force and how buoyant force is related to weight and tension 


first we tested the amount of buoyant force by tension and weight of the metal object, after calibrating the weight of the metal object above water was about 1.962 N +_ .05 N; after the object has fully submerged underwater the reading of the objects weight was about 1.75 N +_ .2 N


we can say that the tension plus the buoyant force should be equal to the weight of the object
                                                           W = T + B


with that comes out to B = .21 N +_ .05 N

we then measured the weight of an empty beaker and when it was filled with water, this gives us the mass of the beaker, water and the combination of the two.  




beaker weight .0995 kg +_ .005 kg
water weight .7375 kg +_.05kg
combination  weight .837 +_.06kg


from this we can calculate the weight of the displaced water and this should be equal to the buoyant force B
which is about .19 N +_ .05N


the volume method 


volume of the cylinder is given by the eq 
                                                                        pir^2h


we can use the vernier caliper to measured the radius and height of of cylinder 
r .019 m +_ .002m
h .045m +_ .005m


from that we can found out the volume of the cylinder and with the weight of the displaced water and the density of the water 1*10^3
we get that the displaced water weight should be something close to the buoyant force about .19 N


analysis 


the three values were quite close to one and another i would assume so because if the experiment was done with 100% precision then the value of B should be the same in all three experiments, but since that can be never achieved, approximation is all we can get, which quite good in this case. 


the weight sensor has to be the most accurate way, there are a lot less uncertainties to worry about ie spills of water out of the cup, estimation of length and radius of some equipment, and the computer software logger pro can take data for every .1 second maybe even less where as human can only do so every couple of seconds


if in the weight sensor experiment the metal cylinder was touching the bottom of the water container this would have changed the reading of B much greater, cause if the object is sitting or even just touching it would reduce the amount of tension that the spring is giving, you would expect the values of B to go up.