(updated: 9/24/2021) Objective: In this lab you will use an oscilloscope. a spectrum analyzer, and a function generator to investigate the characteristics of sine waves in the time domain [history graph] and the frequency domain. You will explore the effects and re latiohships orfrequency, phase, amplitude, linear superpositinning, and nuns linear modulation (product). You will also explore the significance of decibels. As requested, it will be important to label the graphs properly lncludingthe nu merical values and dimensions. Graphs generated by the app Will be mostly lac beled, but you may want to add some additional annotations to the graphs, or notes on the side. It is much preferred and easier to let the Soundcard Scope app plot the graphs, but lf for some reason you are unable to do that, you may plot them by hand on the attached graph paper. At the end of this lab is an appendix which exs plains how to download the plots and data from Soundcard Scope. The plots must be attached to this lab. Procedure, Questions, and Plots: 1. Open up Suundcard Scope by c. Zeitnitz 2. 0n the settings tab, set both output and input audio devices to scope loop- hack. 3. Go to the signal Generator tap. a. Select sine wave for both channel 1 and channel 2. b. Set the amplitude (A) or both channel 1 and channel 2 to .511, and the frequencies to SOOH'z. c. At the lower rightshand corner set the phase offset, deg, to 50". d. Turn on both channels (green arrows on top) A. Go to the Oscilloscope tap. a. Drag the little cross cursor to the leftmost on the center xsaxis. le. Put it at the {0,0} position. b. When the cursor is right at the origin the threshold will he 0 c. Set the trigger to auto, channel 1, rising edge. d. Set channel mode to single. a. Set ampiitucfs sensitivity to 100 mV per division. f. Set timebase to Ants screen slte. g. The channel mode should be at single, h. Note that the two waveforms should have different colors. You can set this with the color bus on top ofthe plot. stretch 1: sketch or print out the two waveforms. tarsal the time asis (its axis) and put in values. Label the amplitude axis ly-axisi and put in values. You may sketch these by hand on the graph paper provided. oryau can use the app to print out the waveform, but you must label them as requested. In: what fraction of a cycle is the offset between channels 1 3t 2. what is this offset in radians. 5. Click the channeimade to cm + CH2. 5. Set the amplitude sensitivity to mm: per division. Sketch 2: Sketch or print out this resulting waveform, and as before label the film: arms. In: what is the frequency ofthe new signal. You can go to the measure box at the bottom and select cursors, time. This will allow you to measure the period accurately by settingthe cursors one period apart. The app will also calculate the frequency which corresponds to that period. This is a simple conversion which was introduced at the beginning of our study of wave theory. 113: What is the peak amplitude (max level above the xax'is) of the Chi + Ch2 waveform. Swltching the cursors to voltage will allow you to measure the amplitude accurately. on: Look up the trigonometric identity for sin u t sin v and write it down. (sosmath.mrn ls a convenlent wehslte for this, but there are many other sources). Note that u and v in this case simply represent the variables of the sine functions and are to be replaced by the appropriate variables of the problem being considered. These have nothingto do with linear den sity and velocity which were also studied in this chapter. as: Express your two CH1 and CH2 waveforms using the form Asinlnn+e). Remember, channel 1 is the reference with zero offset ca.,=o), and channel 2 is offset relative to channel 1. Put in the correct values for in and B. Throughoutthis experiment we are looking at a history graph assuming that e=0, hence the dlsplacement parameter lot is eliminated from the travs ellng wave equation and we only need to worry about the time parameter wt and the phase parameter El. [15: Using the trig identity plug in the actual amplitude, frequency and phase values for your two waveforms (ie. u:t.ot+es. etc.) and simplify the results to the resultant Asin(t.ttta) expression re presenting the sum of the two waveforms. The answer is not evaluated at any specific time.- hence it will still be an expression as a function of t. Q7: Conrm that your new expression for the sum ofthe two waves corre lates with your oscilloscope plot in amplitude, frequency, ond'phase oset. List these 3 parameters. 7. Put the channel mode back to single. 8. Go back to the signal generator tab. a. change the 'equency of channels to 5mm. b. Change the phase to 0 deg. 9. Go back to the oscilloscope lab Sketch 3: Sketch or print out the two waveforms on graph paper label the anes. Label the period (in ms) of each waveform on the sketch. Use the cursors to measure the time. (13: Show that your measurements are consistent with the relationship f:1/T 10. Change channel made fa EH1 #- CH2. Setch A: sketch or print out the waveform on graph paper. Laltelthe cures. Q9: Explain, in your own words, what you see happening with the sum of the two waveforms 11. Set the channel made to CH1 X CH2 Sketch 5: sketch or print out the waveform. Label the axes. Qll): Explain, in your own words, what you see happening vvith the product of the two waveforms. Q11: Look up the trig identity for sin ti sin v. Write it down