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$\bullet$ A person is playing a small flute 10.75 $\mathrm{cm}$ long, open atone end and closed at the other, near a taut string having a fundamental frequency of 600.0 $\mathrm{Hz}$ . If the speed of sound is$344.0 \mathrm{m} / \mathrm{s},$ for which harmonics of the flute will the string res-onate? In each case, which harmonic of the string is inresonance?

The string and the flute will be in resonance when$n_{f}=3 N$ where $(N=1,3,5, \ldots)$$n_{s}=4 N$ where $(N=1,3,5, \ldots)$

Physics 101 Mechanics

Chapter 12

Mechanical Waves and Sound

Periodic Motion

Mechanical Waves

Sound and Hearing

Cornell University

Simon Fraser University

University of Sheffield

Lectures

08:15

In physics, sound is a vibration that typically propagates as an audible wave of pressure, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the reception of such waves and their perception by the brain. Humans can only hear sound waves as distinct pitches when the frequency lies between about 20 Hz and 20 kHz. Sound above 20 kHz is known as ultrasound and has different physical properties from sound below 20 kHz. Sound waves below 20 Hz are called infrasound. Different species have different hearing ranges. In terms of frequency, the range of ultrasound, infrasound and other upper limits is called the ultrasound.

04:49

In physics, a traveling wave is a wave that propogates without a constant shape, but rather one that changes shape as it moves. In other words, its shape changes as a function of time.

07:41

A person is playing a smal…

04:27

CP A person is playing a s…

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04:07

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A violin string $30.0 \mat…

01:36

A violin string $15.0 \mat…

10:11

The 64.0-cm-long string of…

06:29

One string of a certain mu…

02:24

04:17

A violin string $30.0 \ma…

00:49

A guitar string oscillates…

02:48

A violin string 15.0 $\mat…

So we're told the person is playing a small flute that is 10.75 centimeters long. Open up one end and closed at the other near a taut strings having a fundamental frequency of 600 hertz if the speed of sound is 344 meters per second, for which harmonics of the flute with a string resonates. And then, in each case, which harmonic of the string is in residence. All right, so we got our flute committing some sounds and we had our our string over here are taught string and it has some natural frequencies and there's some frequencies come out here and they want to know when these frequencies I'm excited, these frequencies. So we know the velocity of sound and air the length of the flu, their frequency of, uh, the frequency of the string or the fundamental frequency of the string and then we can get our fundamental frequency of the flute is the speed of sound and air divided by four times its length. And that turns out to be a nice round 1600 hertz. Now what we want to do here Yes, we know that the um, the harmonics of the flu. Okay, so these over for L. A times. If n isn't any energy, the Sonics go as one, 35 So we can write that as to end minus one so that this is the the harmonic number off the flute. And if we confide that by the frequency of the fundamental frequency of the string, we need that to be, that would be the harmonic of the string. And we need that to be an energy. So we needed to work out that if we plug in and hear that this has to come out to be an energy so we can fiddle around with that and we can find that that happens when Ennis 258 I win. Harmonic of the flu is 39 15 and so on. And then f turns out to be in those cases. So when an F is three and s is four when the NFL nine n s is 12 when N. F 15 s is 20 and so on

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