Go to https://phet.colorado.edu/en/simulation/fourier and run the spectrum simulator from the website or download and run it on your computer. This is what you should see: Fourier: Making Waves (3.06) Ele Qrtions Discrete Wave Game Discrete to Continuous 109 909 080 080 080 080 800 080 080 800 000 Preset Functions Function sinecosine Harmonics: 11 Amplitudes 1 3 6 11 Function with in number of harmonics raph controls Function of space () sin Ocos Measurement Tools Harmonics Wavelength toot My x (m) Period tool: Math Mode Math form Wavelength () Expand sum. Sound controls Sound Sum (m) 039 Auto scale Help! Note you may need the latest java installed. If you don't, you may obtain it here: http://www.java.com/en/download/ This simulation is essentially a sound mixer or synthesizer (so make sure the sound is working for you), though its principles apply to all sorts of waves. Each bar on the top panel represents a harmonic frequency, and you can drag each bar up and down to activate a sound (by giving that tone or pitch more amplitude). You can also just enter a number in the overhead boxes to set the amplitude. The second panel shows the waves that you have turned on. The third panel shows the resultant sum wave from when you add everything up. You will notice that on the bottom right, there is a sound toggle, so that you can hear the tone, if you so choose. Below that is a rest button such that you can bring the simulation back to this default screen whenever you like. Part I: Wave Addition On the third wave panel, click on the "Auto scale" box. Set the first harmonic to amplitude 1.00, and set the second harmonic at amplitude 0.5. You have now added a second wave to the first wave. Notice how the second panel shows the two waves, and the third panel shows the addition of those waves. Turn on the sound to listen to the new tone that you've created. As described in Chapter 1 of Ferrand, a pure tone is made up of one frequency, and a complex tone is made up of multiple frequencies. You have just created a complex tone.The plots shown are the wave amplitude on the y-axis and the position of the wave on the x- axis in arbitrary units. The x-axis starts at -0.39 m and ends at 0.39 m. Looking at the third panel, the resultant trough (lowest point) is approximately at -0.12 m, and the resultant peak (highest point) is approximately at 0.12 m. lle Options Help Discrete Wave Game Discrete to Continuous Proser Functions 1.00 950 9.09 909 8.60 606 0.06 0.00 0.00 0.80 Function custom Harmonics: 11 Amplitude 3 7 Function with intrite number of harmonica Graph contro's Function of space () sin O cos Measurement Tools Harmonics OWavelength tool: A, x (m) Period took Math Mode Math form Wavelength (A] Expand sum.. Sound controls Sum (m) Reset All Auto scal Help! Now set the second amplitude equal to the first amplitude. Fourier: Making Waves (3.06) X Elle Options Help Discrete Wave Game Discrete to Continuous 1.00 1.80 0.80 0.06 609 280 6.80 609 090 0:40 Preset Functions Functions custom Harmonics: 11 Amplitude 7 11 number of Graph controls Function of space (x) sin Ocos Measurement Tools Wavelength tool: * ~ x (m) Period tool: Math Moxie Math form Wavelength (A) Expand sum. Sound controls Bound Sum (m) Reset All 0.39 Auto scale Help! Notice how the resultant wave has changed, and if you play it audibly (you should), how the sound has changed.Now change the polarity of the second harmonic by setting it to -1.00. This makes crests into troughs, and vice versa. Fourier: Making Waves (3.06] O X alle Options Help Discrete \\Wave Game Discrete to Continuous PHET Preset Functions 1.00 -0.97 10.90 0.00 0.00 0.90 0.00 0.00 0.00 0.00 0.00 Function: custom Harmonica: 11 3 5 11 Amplitudes Function with infinite number of harmonics Graph controls Function of space (x) O sin O cos Measurement Tools Wavelength tool: Harmonics