Use the following interactive tool where you can add up to 8 harmonics of a sine wave, observe andhear the result: https://www.compadre.org/osp/EJSS/4487/272.htm?F=1 (Forinash, 2018).The main panel shows the wave form, and the insert shows the corresponding frequency spectrum.With the control buttons you can adjust the amplitudes of overtones, play and reset the waves, andhear the sound. Each case below is a slightly modified versions of what you see in Forinash (2018). introductory sentence about the goal of this part and the tool used. Adjust the inputs asshown below and answer each of the questions. Illustrate each case with screenshots of theresultant wave with insert for the Fourier spectrum of the components. Notice how changing thespectrum of harmonics changes the timbre

.2.1 Set amplitude A1 = 1 and frequency f1 = 262 Hz to hear the sound. Insert a screenshot of the wavein this case. What is the wave shape and its approximate wavelength measured from the graph? (Thex-grid units are in meters). Play the app to measure the period in milliseconds (the running timer is inthe lower right corner), compare to the calculated period of the given f1.2

2.2 Press "Reset", and choose the same fundamental frequency f1 = 262 Hz, but now set amplitudesA1 = 0, A2 = 1, to hear the second harmonic (f2 = 2f1). What are its wavelength and period? How do thepitches of f1 and 2f1 compare? Illustrate with a screenshot.

2.3 Set f1 = 262 Hz and add the first 4 harmonics, all with amplitude of 1.0. Insert a screenshot anddescribe the resultant wave and the timbre of the new sound (is it bright or dark?).

2.4 Press "Reset", and choose fundamental frequency of f1 = 262 Hz, with amplitude A1 = 1. Add theodd-numbered overtones with decreasing amplitudes (you can type in the numbers in theamplitude boxes): A3=0.33 (or 1/3), A5=0.20 (or 1/5), A7=0.14 (or 1/7), while the even-numberedamplitudes are 0. Illustrate with a screenshot. What is the shape of the wave? How would youcharacterize the sound timbre?

2.5 Press "Reset", choose 0 amplitude for odd harmonics and set the even harmonics as: A2 = 1.0,A4 = 0.25 (or 1/4), A6 = 0.17 (or 1/6). Illustrate with a screenshot. What is the shape of the wave andhow would you characterize the sound?

2.6 Press "Reset", choose the following combination of harmonics: A1 = 1.0, A2 = -0.5, A3 = 0.33, A4 =-0.25, A5 = 0.20, A6 = -0.17, A7 = 0.14, A8 = -0.13. What is the shape of the wave and how would youcharacterize the sound? Illustrate with a screenshot

.2.7 Press "Reset", and synthesize a sound wave with your choice of fundamental frequency f1, andselection of amplitudes of harmonics. Show the screenshot and describe the wave and its Fourierspectrum. How will you characterize the sound?

References

:Academo. (2016). Spectral Analyzer. Retrieved June 14, 2022, fromhttps://academo.org/articles/spectrogram/

and https://academo.org/demos/spectrum-analyzer/Chrome Music Lab. (2019). Retrieved March 21, 2019, fromhttps://musiclab.chromeexperiments.com/Forinash, K. Sound: An Interactive eBook on the Physics of Sound. (2018).

Retrieved June 14, 2022,from https://www.compadre.org/osp/EJSS/4487/272.htm?F=13