Introduction to Sound

Purpose
     The purpose of this lab is to be able to analyze the different sound wave. This lab will also make us to be able to recognize the effect of pitch and volume to the graph of the sound waves.

Experiment
    The setup of experiment is as follow:

Experiment for the part using tuning fork

The setup of the first one is by one person saying "AAAAAAAAAAAA" and then the sound waves is recorded as follow:

figure 1. The sound wave from my lab partner

1. The wave appears to be periodic since the shape repeats as time goes.
2. The waves shown in the sample above has 7 waves. This can be determined by counting the number of the same shape of the waves.
3. The probe only took 0.03 seconds to get this data. It is like 1/10th of a google search.
4. The period of the cycle appears to be 0.0038 s. This can be determined by looking at the time it takes for 1 cycle to complete
5. The frequency on the sample appears to be 262 Hz by using the formula f = 1/T
6. By using the formula lambda =  velocity  /  frequency , the wavelength is calculated to be 1.298 m.
7. The amplitude of these waves appears to be 2.468. This is obtained by taking the average of the smallest amplitude and the largest amplitude in the waves.
8. If the graph is 10 times longer, the only things that changes is the number of waves obtained

figure 1h.  The graph when time taken is 0.3seconds

figure 2. The graph of my other lab partner

1. The number of waves in this sample is only about 4 lower than sample 1
2. The frequency of this sample is 133Hz lower than sample 1
3. The period of this sample is 0.00752s greater than sample 1
4. The wavelength for this sample appears to be 2.56m
5. The result makes sense since sample 2 is done by a male student which have lower pitch while the first one is conducted by a female student which have a high pitch.This makes some difference in the frequency, wavelength and period in the sample.                                          

After the human voice was used, a tuning fork is now used and the graph was taken

figure 3. Graph of the sound waves of tuning fork

Compare to the human voice graph in figure 1 and 2, the tuning fork has a perfect sinusoidal waves. This happens because tuning fork is set to have only one frequency. In human voices, there will be some different frequencies and the one that is been captured is the resonant frequencies of our voices. 

When the volume or intensity of the sound is lower than the previous, the only thing it will change is the amplitude as shown in the picture below:

Figure 3h. Graph of tuning fork with lower volume

As seen in the graphs, the only thing that is different is the amplitude. The frequency, period and wavelength is the same.

Discussion

           Through this lab, we know that sound waves is a periodic waves. Moreover if there only one frequency, like in tuning fork, it will show as a perfect sinusoidal waves. In human voices, even the simplest sound have more than one frequencies and it is shown in the graph that it is a resonant frequency that is being recorded. Furthermore we know some changes that could affect the sound waves. The pitch of a person change the frequency, wavelength and period, while the change in volume or intensity of the sound only changes the amplitude of the waves

Standing Wave

Purpose
      The purpose for this experiment is to be able to observe and analyze standing waves created using oscillator. We will also analyze the effect of tension on the string to the standing waves. In this lab, the wavelength, nodes and frequency will be recorded.

Experiment
      The setup for this experiment is as follow:

This show how we setup one end of the string

The other end of the string is attached to an oscillator

Once the setup is ready, experiment is conducted. The following is the observation seen in the experiment :

This shows one of the node in the string

Length between nodes are obtained to measure the wavelength

The data taken is as follow:
     

f(Hz)	#of node	L between node(cm)	wavelength (cm)	n
21 ± 1	2	61 ± 0.5	122 ± 0.5	1
43± 1	3	30.5 ± 0.5	61 ± 0.5	2
64± 1	4	20.313 ± 0.5	40.63 ± 0.5	3
85± 1	5	15.25 ± 0.5	30.5 ± 0.5	4
108± 1	6	12.2 ± 0.5	24.4 ± 0.5	5
129± 1	7	10.17 ± 0.5	20.34 ± 0.5	6
152± 1	8	8.714 ± 0.5	17.43 ± 0.5	7
174± 1	9	7.625 ± 0.5	15.25 ± 0.5	8
195± 1	10	6.778 ± 0.5	13.56 ± 0.5	9

This data is taken when we put the mass = 551 ± 1 g which gives

 Tension = 5.396 ± 1 N

 Length of string = 61 ± 0.5 cm

 v = 26.62 ± 0.75 m/s

The second run is also done by changing the tension of the string. We change the tension on the string by changing the hanging mass to  300 ± 1 g which will also change the tension:

Tension = 2.94 ± 1 N

 The data taken is as follow:

f(Hz)	#of node	L string(cm)	wavelength (cm)	n
16 ± 1	2	61 ± 0.5	122	1
32 ± 1	3	30.5	61	2
48 ± 1	4	20.313	40.626	3
64 ± 1	5	15.25	30.5	4
80 ± 1	6	12.2	24.4	5
96 ± 1	7	10.17	20.34	6
112 ± 1	8	8.714285714	17.42857143	7
128 ± 1	9	7.625	15.25	8
145 ± 1	10	6.777777778	13.55555556	9

v = 19.604 ± 0.75 m/s

Questions:

1. The ratio for wave speed of case 1 compare to case 2 is :26.62 / 19.604 = 1.358
2. By applying equation v = sqrt(T/density), the velocity is obtained and the ratio is calculated to be: 1.354.
3. Based on the data obtained, the frequencies is indeed equal to the formula f = nf_1 where n is the number of the harmonic.
4. The ratio for frequency in case 1 and case 2 is compiled below:

   case1	case2	ratio
   21 ± 1	16 ± 1	1.3125 ± 0.14
   43± 1	32 ± 1	1.34375 ±0.14
   64 ± 1	48 ± 1	1.333333±0.14
   85 ± 1	64 ± 1	1.328125±0.14
   108 ± 1	80 ± 1	1.35 ± 0.14
   129 ± 1	96 ± 1	1.34375±0.14
   152 ± 1	112 ± 1	1.357143±0.14
   174 ± 1	128 ± 1	1.359375±0.14
   195 ± 1	145 ± 1	1.344828±0.14

5. Based on the data the ratio appears to be the same. There are a little difference for each which is caused by the uncertainty of the measurement and some rounding in the calculation.

Discussion

       Through this experiment, we know that the equation for wave speed = frequency * wavelength holds true. This is proven by the graph being linear with the slope being the wave speed. We also know that by reducing tension, the wave speed will also decrease. Some source of the error that could contribute to small difference in the value is the measurement uncertainty, rounding error, and also not all the frequency goes into the string since the string may not attached to the oscillator completely especially as frequency increase.

Fluid Dynamics

Purpose
       The purpose of this lab is to determine the time required to empty the water in a bucket using the Bernoulli principle. In this lab, the percent error will also be calculated and will be compared to the true value.

Materials

• Bucket with small hole in the bottom
• Water
• Ruler
• Stopwatch
• Beaker

Experiment

The setup for the experiment

Once the setup is ready, the experiment is conducted and time to empty 16 ounces of water is taken. The following is picture of how the experiment is conducted:

The reason 2 beakers are used is because one beaker can only contain 400mL while we need 450mL. The time taken to empty the 16 ounces was then measured to be:

1st =44.85s

2nd =45.35s

3rd =44.34s

4th =45.67s

5th =46.39s

6th =46.17s

Once the time is recorded, the average of the six run and the standard deviation was calculated and the result appears to be:

      t = 45.46 ± 0.7812s

In step 3 of the experiment, theoretical time is calculated using the following data:

     Volume emptied = 16 ounces / 998.83 ounces/ft^3 = 0.016 ± 0.000845ft^3

     Diameter of drain hole = 0.40 ± 0.005 cm

     Area of drain hole = 0.000135 ± 0.000003375 cm²

     Acceleration due to gravity = 32ft/s²

     Height of water = 1.8 inches = 0.15 ± 0.00417ft

By using the data above, the theoretical time can be calculated using the formula  t=V/A*√2gh.

By using the formula:

    t_th = 38.25 ±7.65 s

The percent error of the time was then calculated and appears to be 18.8%

Some of the error that may happens are the beaker used in the experiment is not an accurate tool to measure the 16 ounces of water. The use of 2 beakers might also contributes to the error since some of the water might actually got spilled instead of being contained. There might also be error contributed through the use of wet beaker instead of the clean and dry one since it change the time by a little bit.

In step 4 of the experiment, the diameter of the drill is actually calculated by deriving it from the formula used for the theoretical time.

The calculated diameter was calculated to be 0.366  ± 0.165 cm

The percent error of the diameter appears to be 9.17%

Through this experiment that Bernoulli equation can be used in an experimental lab since the results show that the the true value lies inside the uncertainty of the experimental value. Since the true value is in the uncertainty and the percent error is fairly low, the data can be concluded to be quite accurate.

Fluid Statics

Purpose:

      The purpose of this lab is to determine the buoyant force that is being applied to a metal cylinder using 3 methods: underwater weighing method, displaced fluid method, and volume of object method. This lab will also observe the accuracy of each method using uncertainty and error analysis.

Equipment:

• Force probe
• String
• Overflow can
• Beaker to catch overflow
• Metal cylinders with hooks or tie with string
• Meter stick
• Vernier caliper or micrometer caliper

Part A: Underwater Weighing Method

      In this part, the metal cylinder was weight was determined in air to be 1.154 N. Once it was determined, the setup below is conducted.

The experiment conduct

In the picture above, you can see that the metal cylinder is hooked on a string to the force sensor and the data is taken on the laptop which shows the value of 0.07766N. The free body diagram of the metal cylinder is shown below

Free body diagram of metal cylinder in water

According to the free body diagram: 

where mg = 1.154 ± 0.0005N, and T = 0.7766 ± 0.00005N

Thus, conclude B = 0.3774 ± 0.0001878N

Part B: Displaced Fluid Method
         In this part, the mass of dry, empty beaker is measured to be 0.14368 ± 0.000005kg. And then the following procedure is done.

1. Graduated cylinder fully filled with water

2. Metal cylinder is inserted into the graduated cylinder

3. The overflow contained in the beaker

4. Measure the mass of the beaker+water, which is 0.18133 ± 0.000005kg

Using these information we can calculate the mass of the water which comes to be 0.03765 kg.
According to Archimedes' principle, the buoyant force is the weight of the water which appears to be:
B = 0.369347 ± 0.00002304N


Part C : Volume of Object Method
        In this part, the volume of the metal cylinder is measured using caliper. The data obtained is as follow:
     h = 0.0691 ± 0.00005 m
     d = 0.0260 ± 0.00005 m
     density of water = 1000kg/m^3
     g = 9.81 m/s²

from the data obtained, the buoyancy can be determined
 B = 0.35990 ± 0.001645 N


Questions

1. The Buoyant force of the three method appear to be closely similar. Some discrepancy in the values may be caused by error created in the method such as in method 2, some water might not totally flow into the beaker instead stick on the surface of the graduated cylinder. They all also pretty accurate since the uncertainty is only around 1% of the value calculated.
2. I think the most accurate method is the underwater weighing method because there are not much room of error since it is all measured by computer. Although it have greater uncertainty than method 2, as said in number 1, method 2 could create error such as the water sticking to the surface of the graduated cylinder. I think method 3 is the least accurate one since there will be errors on the measurement and the third method has the most measurements required which means uncertainty also increases.
3. If the metal had been touching the bottom of the water container, the buoyant force will have been too low because the force acting on the object will increase in numbers. The normal force created will adds up to the upward force which will make the buoyant force decrease to be in equilibrium.