1. The beats you observed in Run 3 resulted from the overlap of sound waves from the two tuning forks. How would the data you recorded compare to a simple addition of the waveforms from the forks individually? If the sound waves combined in air by linear addition, then the algebraic sum of the data of the individual waveforms should be similar to data of the beats. The following steps will help you perform the addition: a. Show Run 3 only (the waveform of the actual beats). b. Choose New Calculated Column from the Data menu. Give the column the name of "Sum." c. Click once in the equation field to place the cursor there. Choose Run1 :Sound Pressure from the Variables (Columns): menu, type the addition symbol "+", and choose Run2:Sound Pressure from the Variables (Columns) menu. The resulting equation will read "Run1 :Sound Pressure + "Run2:Sound Pressure". d. Click Done. Click No if Logger Pro asks if you want to select a specific Data Set. e. A new column, representing the sum of the two waveforms, will be created in each Data Set. f. Drag the Sum column header of Run 3 from the data table area to the y axis area to plot the Sum column. g. Click on the y-axis label to show the y-axis selection dialog and uncheck all but the Sum column in Run 3. Click | ox . You now see the mathematical sum of the Runs 1 and 2. Rescale the graph if needed. Now use the y-axis label dialog to display only the actual data of the beats. (It is hard to see with both plots on screen at once, so look at one at a time.) How is the sum similar to the real data? How are they different? Do the graphs support the model of additive sound wave superposition? What if the superposition rule were multiplicative? Would that change the graph? 2. There are commercial products available called active noise cancellers, which consist of a set of headphones, microphones, and some electronics. Intended for wearing in noisy environments where the user must still be able to hear (for example, radio communications), the headphones reduce noise far beyond the simple acoustic isolation of the headphones. How might such a product work