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$\bullet$ Voiceprints. Suppose a singer singing $\mathrm{FH}$ (370 Hz, thefundamental frequency) has one overtone of frequency 740 $\mathrm{Hz}$with half the amplitude of the fundamental and another over-tone of frequency 1110 Hz having one-third the amplitude of the fundamental. Using the previous problem as a guide, graphthe superposition of these three waves to show the complexsound wave produced by this singer.

Now, the superposition of these three waves is given by$y_{1}+y_{2}+y_{3}=\sin \left(2 \pi f_{1} t\right)+\frac{1}{2}\left(2 \pi f_{2} t\right)+\frac{1}{3} \sin \left(2 \pi f_{3} t\right)$$=\sin (740 \pi t)+\frac{1}{2} \sin (1480 \pi t)+\frac{1}{3} \sin (2220 \pi t)$

Physics 101 Mechanics

Chapter 12

Mechanical Waves and Sound

Periodic Motion

Mechanical Waves

Sound and Hearing

Rutgers, The State University of New Jersey

Hope College

University of Winnipeg

McMaster University

Lectures

04:16

In mathematics, a proof is…

04:48

In mathematics, algebra is…

03:33

$\bullet$ Voiceprints. In …

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A violin sounds a note of …

00:52

If two successive overtone…

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Analysis of the periodic s…

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A flute acts as an open p…

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If the fundamental frequen…

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A person is playing a smal…

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On a standard piano, the A…

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(I) If a violin string vib…

So it's pulled a singer singing F H four Fundamental frequency 370 hurts has one overtone of frequency twice the fundament also 740 hurts but have the amplitude of the funnel for off the fundamental frequency and another overtone that, um 1100 10 hertz which would be the third harmonic, having 1/3 the amplitude of the fundamental and using the previous problems guide draft A superposition of these waves wave produced by the same. So we have our our three frequencies are fun of my art, our fundamental harmonic, our second harmonic and our third harmonic overtones. And then we had we know that the aptitudes of the second harmonic is half that of the first and my money 1/3 of that of the first. We can actually make some plots here. So when I spotted as these are all of the 33 harmonics individually. So we have our first harmonic with an amplitude of one unit. Our second harmonic, which is has twice the frequency and 1/2 the amplitude and our third harmonic, which has three times the frequency and 1/3 the And if we had is altogether and plot the some of them. We get a wave that looks like this, which is not at all sign your soil but quite complex goes up kind of. It's almost like a saw.

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