Section 001

Experiment 2

Date performed 1.29.07

Date due: 2..07

THE OSCILLOSCOPE

Principal investigator: ___________________________________________________

Skeptic: ____________________________________________________

Researcher ____________________________________________________

TA ____________________________________________________

Role I DC AD RC Q1 Q2 PI PG

I introductionDC data and calculationAD analysis and discussionRC results and conclusionQ1/Q2 quiz/prelabPI principal investigator pointsPG personal grade

I. Introduction

The goal of this lab was to learn how to use the Oscilloscope and become familiar

with using the apparatus for future experiments. The Oscilloscope, often referred to as an

O-scope is a machine that can calculate the voltage of a system over a certain amount of

time. This measurement is then given in the form of voltage versus time graph. Becoming

familiar with the apparatus now will give us the experience we need to use the O-scope

with ease.

The first step in this lab was familiarizing ourselves with the volts/division knob

and the time/division knob. Each of theses knobs changes the scale of the O-scopes

measurements. In this step the researcher adjusted the volts/division knob and the

time/division knob to their lowest settings. The skeptic then read these values and

transferred the information to the PI who processed the information into an excel

spreadsheet. The volts/division knob and the time/division knob were then set on their

highest setting and the procedure was repeated.

In the next step of the experiment, the function generator was set to 500 hertz to

give a sine wave by the skeptic. The researcher then adjusted the time/division knob so

that the graph showed roughly ten cycles. The skeptic then measured the peak to peak

distance and calculated the root mean squared voltage. The PI recorded frequency, the

volts/division, the Y-deflection, the peak to peak voltage of the wave, the voltage from

origin to trough and the root mean squared voltage in an excel table. This process was

repeated two more times with frequencies of 1,000 and 1,200 hertz.

In the third and final step of the experiment the function generator was again set

to 500 hertz in the sine wave function by the skeptic. The researcher then adjusted the

time/division so that about ten cycles were on the screen and so each cycle could be

easily read. The time/division was then measured by the researcher. The skeptic then

calculated the period, experimental frequency and percent difference of the generated

frequency and the experimental frequency. The PI then put this data into an Excel

spreadsheet.

The group’s first meeting was right after the lab. The group discussed each others

roles and the data that was going to be sent out via email.

Equipment Used:

1 Digital oscilloscope - #11

1 Sine wave and square wave generator - #FG2135

Reference: Ellis, Steven. University of Kentucky Department of Physics and

Astronomy: Laboratory Manual. 2007 (pgs. 9-13).

II. Data & Conclusions

In the first step of the experiment the smallest and larges values of the volts/division knob

and the time/divisions knob were simply read off the O-scope and recorded. The

uncertainty was then taken as one half of the smallest measurement. The following table

shows these findings.

Part A Min Est. Max Est

Y axis 4 ± 2 mV 10 ± 5 V

X axis 1 ± 0.5 ns 0.2 ± 0.1s

In the second step of the experiment three different frequencies were set from the

function generator. The volts/division was then set to show ten cycles on the screen and

the volts/division was recorded. The distance from peak to trough was measured as well

as the distance from the origin to peak. Finally, the root mean square voltage was then

calculated using the equation . For example when the frequency was

500hertz the Vrms was 3.536 volts ( ). The following table shows

these results.

Part B

Freq.

Hz V/div

Y-

Deflect. Vpp Vp Vrms

1 500 Hz 10 1 10 5 3.536 V

2 1000Hz 10 1 10 5 3.536 V

3 1200Hz 10 1 10 5 3.536 V

In the final step two frequencies were set on the function generator in the form of both

the sine and square waves. The time/division was then recorded as well as the X-

deflection. From these two values the period was then calculated. For example the 500Hz

frequency in the sine wave had a time/division of 2.5 milliseconds and an x deflection

was 1 division. When we multiply the two, the division cancels out and we are left with

the time of our period ( . From this we

can use the equation to solve for frequency. Therefore the frequency of the first

example is 400 Hz ( ). Finally the percent difference between

this experimental frequency and the actual frequency was calculated using

. For the first example this was 22.2% (

). The following graph shows all of these

calculations.

Part C

Freq.

Hz Time/Div

X-

Deflect.

Period

T Exptl. F % Diff.

Sine 1 500 2.5 ms 1 2.5 ms 400 Hz 22.2% 590 Hz

Sine 2 1000 1.0 ms 1 1.0 ms 1 kHz 0%

1.058

kHz

Square

1 500 2.5 ms 0.6

4.166

ms

666.6

Hz 28.5% 590 Hz

Square

2 1000 1.0 ms 1 1.0 ms 1 kHz 0%

1.058

kHz

III. Analysis & Discussion

Original oscilloscope data show uncertainties involved with each measurement.

Errors are present in any empirical measurement and excellent science has to account for

these errors. These result from the researcher on the smallest measure from the

experimental scale. A good example is using a meter stick in a lab and estimating the

amount of millimeters between centimeters for a more precise quantitative analysis.

Error allows for variation in half the smallest increment in the focal scale. These errors

are insignificant and are mentioned to relate human error in the laboratory experiment.

Sample Calculation: error propagation of uncertainties Part A

T = time V = volts D = divisions

Part C showed percent differences rather significant in relative quantitative

comparisons. A point to consider is the fact that there was an analog dial on the function

generator but the oscilloscope shows data digitally.

Sample Calculation: Percent Difference

Such a large percent difference requires further investigation and explanations.

As far as ordering error in terms of significance this is most likely the primary cause of

error in the experiment.

Random errors could be summarized as those mentioned where an analog dial is

adjusted by a researcher.

Systematic errors could be best summarized as old wires with degraded electrical

conductivity due to a number of causes, an older function generator with similar

problems and generally any errors associated the experimental setup.

The following figure shows the relationship between amplitude, frequency and

wavelength all directly related values when quantifying studies on waves.

Figure 1. Graph displaying volts versus time

IV. Results & Conclusions

The empirical results were reasonably close to theoretical quantities. For sine

wave number 1, the percent difference was 22.2 % while the first square wave was 28.5

%. Scaling the error-adjusted data with theoretical data on a number line is an instructive

way to visually see the ranges of pertinent data in an investigation. It should be noted

that for the analog dial on the function generator there was a ± 50 Hz uncertainty for all

theoretical and experimental values.

Figure 2. Number line showing error for sine wave number 1

The above number line with the uncertainties for the experimental values shows

little overlap and therefore hardly any agreement in the data probably due to an old function generator and mentioned possible causes for error.

Figure 3. shows the error for Sine wave 2 on a number line for comparative analysis.

Figure 3. Number line showing error for sine wave number 2

This figure shows strong overlap and agreement in the data with hardly any appearance of systematic or random error.

The square wave errors showed a similar pattern when depicted on a number line as shown in Figures 4 and 5.

Experimental 400 ± 50 Hz Hz

Theoretical500 ± 50 Hz

Experimental 1000 ± 50 Hz Hz

Theoretical1000 ± 50 Hz

Hz 300 350 400 450 500 550 600 650 700

Hz 800 850 900 950 1000 1050 1100 1150 1200

Figure 4. Number line showing error for square wave number 1

Hz 300 350 400 450 500 550 600 650 700

Theoretical500 ± 50 Hz

Significant error is depicted as shown in Figure 4. Random error is probably the cause because this is the only wave where the ranges do not overlap. This test was not accurate as well as this difference does not suggest the predictability of systematic error.

Figure 5. Number line showing error for square wave number 2

Experimental 666.6 ± 50 Hz

Hz 800 850 900 950 1000 1050 1100 1150 1200

Figure 5. shows the final experimental result with square wave 2 which depicts the patterned precision and great accuracy which appears to be exact. According to these data this suggest a excellent experimental setup with no appearance of systematic or random error.

The primary purpose of this experiment was to understand how voltage changes over time in a system, specifically modulated by a function generator. Many applications of these concepts could be understood in terms of recording voltage in any industrial or residential electrical system to understand the depolarization of a neuron based on millivolts.

Another vitally important part of this study was to see how closely experimental data agreed to theoretical data based on quantifiable analyses. Scientific errors were present and accounted for. It was instructive to see how these errors affected the data.

Conclusively, in the second and fourth test, phased waves could explain agreement between theoretical and experimental values. This was a very instructive lab in helping to understand the sine wave relationship between voltage and time. An entire range of reasons could help explain differences in the measurements. Older wires, a problem with the function generator and even disrupting electric fields could have interfered with the experimental setup.

The research team collaborated well together to finish the project in a timely manner and everyone worked tremendously well together.

Experimental 1000 ± 50 Hz

Theoretical1000 ± 50 Hz