Experiment 7: Introduction to Reflection and Refraction

Introduction:
This experiment allows us to observe the effects light traveling from mediums of different densities.

Equipment:

-Light box
-Semicircular plastic/glass prism
-Circular protractor

Procedure:
There were two parts to this experiment. The first consisted of having the flat side of the semicircular prism face the light ray and treat this as an incidence from the air to the glass. In the second part of this experiment, the circular side of the prism was facing the light ray, and we treated this as incidence from the class to the air.

Part 1:

Prior to starting the observations, we made some initial predictions of what would occur, mainly that for the original incidence there would be a zero angle of refraction (perpendicular to normal between both mediums) and that at other incident angles there would be angles of refraction because the densities of both mediums varied. In this first part of the experiment, the light is traveling from the lower density medium (air) to glass. Which means the angle of refraction (respect to the normal) should be less than the incident angle according to Snell's Law.

Part 2:

Similar to the first part, we had to make some initial predictions before starting the experiment. Like the first part of the experiment, the incident angle will equal the refracted angle if the angle of incidence is zero with respect to the normal between the two mediums. This case involves light traveling from a higher density material (glass) to the less dense air. According to Snell's Law, the angle of refraction should be greater than the angle of incidence.

Data/Calculations:
Part1:
Below is a table of the information we gathered for the first part of the experiment.

The following is a graph of theta one versus theta two. It appears you can fit a simple line equation in the order of y = mx + b to it.

The graph below is that of sin theta one versus sin theta two. The regression line for the graph is shown. The slope of this graph is about 1.5, according to Snell's Law, this should be equal to the index of refraction of the glass. The relationship in this straight line deals with how strongly the light will be bent upon reaching a medium with a greater index of refraction.

Part 2:

Similarly, we gather information and record these results on a table.

We had to do certain angles instead of the ones we had planned to (else we wouldn't have gotten ten cases) because we reached the critical angle where none of the light was refracted.

Like the first part, we graph sin theta 2 versus sin theta 1 and linear fit this. The slope of this line is one, and judging from Snell's Law, this represents air's index of refraction. This is not the same as the equation we found previously because the beam of light traversed the glass before the air in part 2.

Summary:
This lab went quite smoothly even though there were a few sources of error such as not being able to measure angles with ideal precision. Upon looking at the actual index of refraction for these materials, we can see that our experimental values came pretty close.

Experiment 6: Electromagnetic Radiation

Introduction:
We observe the phenomena of electromagnetic waves from a transmitting antenna to a receiver.

Equipment:

-Oscilloscope
-Oscillator
-BNC adapter (point receiver)
-Copper wire (antenna)
-Meter stick

Procedure:

On the oscillator we dialed a frequency of 30kHZ. We changed the time/division on the oscillascope and the voltage/division until we could see a signal on the screen.
To verify that the signal we saw on the oscilloscope was generated by the antenna we performed the following tests:
1. Moving the antenna closer made the wave amplitude larger.
2. Moving the antenna farther made the wave amplitude smaller.
3. Not moving the antenna kept the wave amplitude the same.

We then proceeded to measure the amplitudes at certain equal intervals of distance from the receiving antenna to observe how the wave amplitude varied across this range.

Data/Calculations:
Below is a table containing the data we gathered in this experiment.

Below is a graph of the peak-to-peak amplitude as a function of distance. This scatter plot seems hyperbolic in nature.

Trig Variant:
The first graph is the data fitted with the function A/R while the second one fits the data with A/R^2. The first graph appears to fit the data most accurately.

The final graph below is a fit with the function A/R^n. This fit seems to be on par with a fit of A/R.

Summary:
We would expect 1/r to fit well if the transmitter were a point charge, but because this is simply not true (our transmitter was a copper wire with a certain length). This

Experiment 5: Introduction to Sound

Introduction:

In this experiment we observe and measure various properties of sound waves.

Equipment:

-Loggerpro

-Microphone

-Tuning fork

Procedure:

Two of us tried our best to say "AAAAAAAA" smoothly into the microphone, in the third section of this experiment, we had to use a tuning fork instead. The sound waves were recorded by loggerpro and we got to observe a graphic representation of the waves to calculate some of their various qualities.

Data/Calculations:

Graph for part 1:

Graph for Part 2:

Graph for Part 3:

Graph for Part 4:

Summary:

It was rather difficult to get any decent looking waves in this experiment, especially using our voices because even the most minimal alteration during the process would most likely cause the wave to change.

Experiment 4: Standing Waves

Introduction:
We generated various normal modes and analyzed the various resonant conditions for standing waves on a string.

Equipment:

-Pasco variable frequency wave driver
-String
-Pasco student function generator
-Weight set (grams)
-Pendulim clamp
-Pulley
-Digital Multimeter
-Meter stick

Procedure:

We took some initial measurements (mass and length of the string) and we set up the system. We then took various measurements for different harmonics (such as number of nodes, antinodes, wavelength) and we achieved such harmonics by adjusting the frequency of the function generator. This was done for two instances, the second of which was equivalent to one-fourth the original tension.

Data/Calculations:

We went through ten harmonics in case one and six in case two by toggling with the frequency generator. We recorded the frequencies that produced such harmonics and length from one node to another to calculate the wavelength. We also counted the number of nodes and anti-nodes and recorded them on the table above.

Above are the graphs we created by plotting the frequency versus one over the wavelength, the graph's slope should equal the wave speed.

We calculated the experimental values for their respective velocities using the formula shown above.

Above are the wave speeds from the graph and the wave speeds we calculated respectively. The experimental and theoretical values both seem to vary by a factor of two.

We can see from the table above that the experimental value of frequencies is around n times the frequency of the fundamental. Where n is the number of the harmonic.

The table above is obtained from taking the ratios between the frequencies in the first case and the ones in the second case. They also seem to differ by a factor of two.
Summary:
This experiment was surprisingly very accurate when comparing the values obtained from formulas and the values obtained from our observations. There are many factors that make them differ, however, such as wind resistance and the fact that we where conducting this experiment in a three dimensional space (the string not only oscillated, but also sort of spun in circles).

Experiment 3: Frequency and Wavelength

Introduction:
In this experiment we determined wavelength as a function of f and found the relationship between frequency and wavelength.

Equipment:

-Long slinky-like coil (to generate waves)
-Meter stick
-Stopwatch

Procedure:

In this experiment we decided that we would measure set distances and create waves and count how long it would take for the system to repeat ten cycles of complete wavelength so we could divide this number by ten for an accurate period (T).

Data/Calculations:

We collected data for five different distances and we did three iterations on each case for further accuracy. We then took the averages of these values and divided them by ten to find the period. We calculated the frequencies from these periods and graphed the information on loggerpro.

Summary:

Our values in this lab were a bit consistent, but there are still a quite a few significant sources of error such as gravity, air resistance, and other less than ideal conditions such as being unable to measure the precise timing for ten wavelength cycles.

Experiment 2: Fluid Dynamics

Introduction:
In this experiment, we utilize Bernoulli's equation to calculate the time it takes for a certain amount of liquid to exit a container through a small hole located near the bottom of the container and we compare the result to a physical simulation of such an instance.

Equipment:

-Bucket (with a hole near the bottom)
-Water
-Timer
-Ruler
-Bottle with volume marks

Procedure:

The physical simulation was to be done for six instances in which we approximated the time for 300mL of water to exit the bucket through the small opening.

Data/Calculations:

Summary:
This experiment shows that even the smallest miscalculation in the measurement of the diameter of the hole from which the water flows out of can create a very significant percent error. Another very significant source of error is the timing, because it was very hard to measure precisely how long it would would take for the water to flow out, especially when it took such a short amount of time.

Experiment 1: Fluid Statics

Introduction: 
In this experiment we estimated the buoyant force using three different methods. Then we compared the results to see which one might have been more accurate.

Equipment:
-Force probe
-String
-Overflow can
-Beaker (to catch overflow)
-Metal cylinders (with hooks or tied with string)
-Meter Stick
-Vernier or micrometer

Procedure:
A) Underwater Weighing Method
We measured the weight of the metal cylinder in the air then while it was completely submerged in water using a force probe and logger pro. The buoyant force can then be calculated by taking the difference of the two resulting string tensions.

B) Displaced Fluid Method
The weight of the beaker used to catch the overflowing water is taken before anything. An overflow can is filled to the top with water and the metal cylinder is placed inside it slowly and carefully. The water will spill into the beaker, when the water stops dripping into the beaker, the mass of both the water and the beaker is measured. By subtracting the mass of the beaker you obtain the mass of the water, by Archimede's principle the weight of this water will be equal to the buoyant force.

C) Volume of Object Method
The volume of the cylinder is approximated and the approximate weight of an equivalent volume of water is calculated from this. By Archimede's principle, this should equal to the buoyant force.

Data/Calculations:
A) Underwater Weighing Method

B) Displaced Fluid Method

C) Volume of Object Method

Summary:
1. Compare your three values for the buoyant force. (treat error analysis and answer the question in terms of uncertainties)
The most accurate answers appear to be the ones where the volume and the displaced water method while the underwater weighing method has a larger error bound. All three methods have their own prominent sources of error. The underwater weighing method does not account for the weight of the string and possible inaccuracies of the force probe. The displaced fluid method can have a few differences in weight measurements. The volume of object method inconsistencies with measurement.

2. Which method do you think was the most accurate and why?
The volume of object method seems to be the most accurate because there is less room for mistakes, whereas in the other two methods we had to rely on a lot more than a few measurements to calculate volume.

3. In part A, if the cylinder had been touching the bottom of the water container, how would that have changed your value for the buoyant force? Would your value have been too low or too high? Explain.
The weight of the metal cylinder would have measured to be significantly smaller underwater and this would have resulted in a higher value for the buoyant force.