Experiment 7: Introduction to Reflection and Refraction

The purpose of this lab was to study the properties of reflection and refraction using semicircular prism and a source of light.

In this experiment we used:

- Light box

- Semicircular prism

- Protractor

PART ONE:
First we adjusted the light box so that the light waves entered the flat part of the semicircular and exited the curved part. We taped a paper protractor under it so that the center of the flat side was on top of the protractor and on the 0 and 180 degree line. We then turned on the light box and recorded the angle of incidence θ1 and the angle of refraction θ2. We then rotated the prism  and protractor (together) by 4-8 degrees and measured the angles. We did this for a total of ten trials until we reached 80 degrees.  

 

Below is the data collected:

We recorded the values for theta1 and theta2 and found the sin(theta1) and sin(theta2). We then plotted the sin(theta1) vs sin(theta2). 

 The slope of this graph was 1.9944. This slope is the index of refraction of the material that we used. 

PART TWO:

In this part of the experiment we did the same as above except that the light box ray entered the curve part of the semicircular prism and exited the plat side. We recorded the theta1 and theta2 when it was at 0 degrees and then rotated the prism every 4-8 degrees.

We recorded the values for theta1 and theta2 and found the sin(theta1) and sin(theta2). We then plotted the sin(theta1) vs sin(theta2). 

 The slope of the plot is 1.3346 is the index of refraction of the semicircular prism. We were not able to complete all of the trials because at 45 degrees, there was the critical angle where there was no refracted ray.

Conclusion:

The theoretical value for the the index of refraction of the semicircular prism is 1.49.

Experiment 6: Radiation Lab

The purpose of this experiment was to observe and study electromagnetic radiation using a simple antenna.

In this lab we used:
-Copper Wire
-Meter Stick
-BNC Connector
-Frequency Generator
-Oscilloscope

In the experiment, we created a transmitter by attaching a copper wire on to a meter stick using tape. One end was connected to the frequency generator. We then created a receiver by plugging in at the BNC connector into the oscilloscope. We then ran a 30 Hz frequency with a maximum amplitude. The time/div was changed to 01. ms and we decreased the voltage/div until we observed a signal on the screen. We then recorded the peak to peak amplitude of the electromagnetic wave for several trials.

Below is the data that was collected:

We then plotted the peak to peak amplitude as a function of distance:

CONCLUSION:
The graph was inverse proportional. We fitted the A/r and the A/r^2 to the graph. The A/r fit was better than the A/r^2 even though it is not a perfect fit. The best fit was A/r^n. We expected that the A/r function, but since it was not a point charge, we had to take into consideration the dx because the transmitter was linear perpendicular to the receiver.

Experiment 5: Introduction to Sound

The purpose of this lab was to observe the properties of sound waves using a human voice and a tuning fork.

We used:
- LabPro
- Microphone
- Brave student
- Tuning fork

PART ONE:
A brave student showed off his vocal skills by saying "AAAAAAAHHHHHH" smoothly into the microphone for 0.03 seconds. We recorded their beautiful voice and we saved the graph on LoggerPro. Below is the graph we obtained.

Below are the answers to the questions about the sound wave obtained.
a) The wave is periodic because although it is not a perfect sinusoidal wave, it has sinusoidal wave properties that repeat it self in a periodic manner.
b) There are about 4.8 waves in this sample. I determined it by counting the number of times the highest wave in the period appeared.
c)We recorded the sound for 0.03 seconds. This is similar to the amount of time that the brain takes to recognize a sound.
d)The period of this wave is about 0.00623 seconds. This is the time that we recorded the waves for, 0.03 sec, divided by the number of waves during that time, 4.8.
e)The frequency is 160 Hz. This is 1/T, where T is the period of the wave.
f) The wave length is lambda=v/f. This is equal to (340 m/s)/(160 Hz)= 2.125 m. This is about the distance from Professor Mason to the first row of desks in class when he is lecturing.
g)The amplitude is 1.543 arbitrary units. This was determined by the graph.
h)If we had recorded for 0.30 seconds, we would have a lower arbitrary amplitude, but besides that nothing else would change because the period of the wave is not changing.

The graph below shows how amplitude would change because it is an arbritary value if we recorded for 10 times longer.

PART TWO:

The individual wave patterns are similar because although they are not perfect sinusoidal waves, they are periodic. This wave has about 4.5 waves in 0.03 seconds. This means the frequency for this wave is   150 Hz. The period for each wave is about 0.0067 sec. The amplitude of this wave is 1.512 arbitrary units. The wavelength of this wave is 2.27 meters. The waves are similar in value but the first wave was a lot more smoother.

PART THREE:

Compared to the wave that was produced by a human's voice, the wave that was produced by the tuning fork is perfectly sinusoidal. It is much smoother and has a clear amplitude and frequency. There were 13 waves in 0.03 seconds. The period is 0.0023 seconds. The frequency was 433 Hz and the wavelength was 0.785 meters.


PART FOUR:

To produce a softer wave, we banged the tuning fork on a softer surface, such as the bottom of a shoe. What changed in this wave was that the amplitude of the wave was higher and that there were less waves produced in 0.03 seconds.

Experiment 4: Standing Waves

The purpose of this lab was to investigate resonant standing waves that are driven by a frequency generator.

We used:
- Mechanical Vibrator
- Frequency Generator
- 50 gram hangar and weight set
- String
- 2 table clamps
- Rod
- Pulley
- Meter Stick

Below are a pictures of out experiment:

We first measured the mass and length of the string used in the experiment to find the linear density of the string.

We then assembled the string between the two supports with 200g total mass hanging on the end of the string. When we set the string to oscillate, we adjusted the frequency generator until the string oscillated in its fundamental node. We then recorded the oscillation frequency, number of nodes, the total length of the string participating in the oscillation for the first, second, third, etc. harmonics.  We then reduced the tension on the string to one fourth of its original tension for the second case and repeated the experiment.

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CASE #1:

The above table shows the nodes, frequency, and wavelength of the first case and below is the plot of the frequency versus 1/lambda. 

The slope of the line, 80.233, is the wave speed. Below I calculated the wave speed using the equation for the wave speed. 

The percent error for the wave speed is 29.0%.

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CASE #2:

The above table shows the nodes, frequency, and wavelength of the first case and below is the plot of the frequency versus 1/lambda. 

The slope of the line, 40.103, is the wave speed. Below I calculated the wave speed using the equation for the wave speed. 

The percent error for the wave speed at 1/4 the tension is 28.9%.

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We then calculated the ratios for the wave speeds for case 1 compared to case 2 which is equal to the expected wave speed ratio:

From the above tables for case 1 and case 2, we can see that the measured frequencies are equal to n*f_n, for the harmonics. The ratio of the frequency for the first, second, third, etc. harmonics for case 1 compared to case 2 was 2 as expected. 

The experimental values that we got were not exact, but they were precise because we still got the expected value for the wave ratios and we also had about the same value for our experimental error. The source of error in this lab was the fact that the hanging mass had some movement when the string was oscillating. This meant that at the end where the hanging mass was hanging, there was not an exact antinode for the wave. 

Experiment 3

The purpose of this experiment was to find the relationship between the relationship between the wavelength and frequency.

The above picture describes how we used a metal spring to find the relationship in the spring.

The above video shows how the student created a standing wave.


The Data collected is below with it's corresponding graphs.

Our data did not give us the relationship between the wavelength and frequency that we were looking for. The main source of error in our experiment was the fact that we used a spring that was stretched out in the experiment. This meant that the tension in the string was inconsistent throughout the experiment when it was stretched out.

The relationship that were were trying to confirm with out experiment was:

Experiment 2: Fluid Dynamics

The purpose of this experiment was to use Bernouli's Equation to calculate the time to empty a certain volume of a fluid.

We used a bucket with a whole at the bottom. We filled it up to a certain height and measured it. We the uncovered the initially covered whole and let 200 mL of water flow out of the bucket, while recording the time.

These were the measured times for 200mL to flow out of the bucket:

The measured values during the experiment were:

Volume emptied: 200 ± 10 mL

Height of the water: 13.6 ± 0.1 cm

Diameter of the hole: 0.60 ± 0.1 cm

We then calculated the theoretical time to empty 200mL:

We then calculated the percent error of the time to drain 200mL using the equation from above and tabulated the results:

Assuming that the diameter we measured was wrong, we calculated the "actual diameter" of the whole.  I used the average time to drain from the experiment results:

Conclusion:

When I compared the theoretical value to the experimental value, it did not agree with the uncertainty. The experimental time to drain the fluid was almost twice that of the theoretical value. None of the experimental values agreed with the theoretical value of 4.33 ± 1.69 seconds. Although the experimental values were not accurate, they were precise because the values were all within a second. This large experimental error must have come from the reaction time of the person taking time to start the timer when starting the experiment and the person telling the time taker to stop the timer. Another source of error was that the dh of the bucket as the water drained. We assumed the dh to be negligible compared to the height of the water in the bucket. Our percent error in the drill bit's diameter was 36.7%.  

Experiment 1: Fluid Statics

The purpose of Experiment 1: Fluid Statics was to find the buoyant force three ways and to find which one was more precise.

One was the underwater method where we found the buoyant force using the free body diagram. We measured the weight of the object in the air and submerged in water.

The second was the buoyant force by finding the amount of fluid that the object displaced. We initially measured the weight of the beaker alone when the was filled with water that overflowed when the object dispersed water of its container into the beaker. With a simple calculation, we found the mass of the water displaced. The weight of the displaced water was the buoyant force that acted on the object.

 The third way that we found the buoyant force was by measuring the volume of object. When we found the volume of the object, we knew that the volume of the object is the same as the volume of water that was going to be displaced by it. Once we found the weight of the displaced water, according to Archimede's Principal it was equal to the buoyant force.

Conclusion:
There were many sources of error in this experiment. In the first part, the LoggerPro force measurer could have not been properly calibrated and the string that the object was held with was not a mass-less string. In the second part of the experiment, a possible source of error could have been that the beaker was not one hundred percent full in the overflow spout. Another error for part two could have been that the object could have caused too much of a disturbance when the object was placed in the water making more water overflow. For the third experiment, there could have been possible source of error when the caliper was used to take measurement of the object's dimensions. Since all the obtained forces of buoyancy agree within the boundary of uncertainty, the values that we got are the same within the error uncertainty. I believe that the third method was the most accurate because it is the one with the least error and there was less propagation of error because there were only two measurements taken. If the cylinder would have been touching the bottom of the water container, it wouldn't have changed the buoyancy force because we calculate the buoyancy force using the volume of the fluid that it displaces. This doesn't depend on the depth that the object is submerged in as long as it is completely submerged.