Hearing Difference Tones When a musical instrument creates a tone of 110 Hz,it also
Chapter 6, Problem 59(choose chapter or problem)
Hearing Difference Tones When a musical instrument creates a tone of 110 Hz,it also creates tones at 220, 330, 440, 550, 660, . . . Hz. A small speaker cannotreproduce the 110-Hz vibration but it can reproduce the higher frequencies, whichare the upper harmonics. The low tones can still be heard because the speakerproduces difference tones of the upper harmonics. The difference between consecutivefrequencies is 110 Hz, and this difference tone will be heard by a listener.(Source: Benade, A., Fundamentals of Musical Acoustics, Dover Publications.)(a) In the window 30, 0.034 by 3-1, 14, graph the upper harmonics representedby the pressureP =12sin32p12202t4 +13sin32p13302t4 +14sin32p14402t4.(b) Estimate all t-coordinates where P is maximum.(c) What does a person hear in addition to the frequencies of 220, 330, and 440 Hz?(d) Graph the pressure produced by a speaker that can vibrate at 110 Hz and above.
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