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Why do higher harmonics have a lower amplitude than the fundamental frequency?

Why not calculate it? Consider a string of length $L$, with its ends fixed at $x=0$ and $x = L$. Let's assume for convenience that at time $t=0$ the string is "plucked" at $x = L/2$, so that ...
Puk's user avatar
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46 votes
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How are overtones produced by plucking a string?

The only way to avoid overtones would be to pluck the string in such a way that its initial shape is sinusoidal. However, that would be nearly impossible. In practice, the initial shape is almost ...
S. McGrew's user avatar
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26 votes

Why do higher harmonics have a lower amplitude than the fundamental frequency?

The answer is actually very dependent on how you pluck the string. If you pluck it closer to the center, you put more energy into the lower modes. Pluck it near either end, and you have more higher ...
Cort Ammon's user avatar
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25 votes

Feynman claimed "The ear is not very sensitive to the relative phases of the harmonics." Is that true?

What Feynman means by that statement is that the "ear" (cochlea) is a spectrum analyzer with a large set of very narrow band filters each followed by a square law (energy) detector, that is ...
hyportnex's user avatar
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21 votes

If all harmonics are generated by plucking, how does a guitar string produce a pure frequency sound?

Usually, a guitar does not produce a pure tone/frequency. If so, its sound would be very close to a diapason. The difference between noise and a musical tone is not that a unique frequency makes a ...
GiorgioP-DoomsdayClockIsAt-90's user avatar
18 votes

Why do higher harmonics have a lower amplitude than the fundamental frequency?

It's simple energy conservation. With an increase in harmonics, the frequency of vibration of the string increases. We know that each particle in the string is executing a simple harmonic motion with ...
Rishab Navaneet's user avatar
15 votes
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If all harmonics are generated by plucking, how does a guitar string produce a pure frequency sound?

Human perception is involved here because when you humans talk about noise this generally means a sound that is aperiodic. However the tone produced by a guitar will be something like: $$ A(t,x) = \...
John Rennie's user avatar
15 votes

Why is the energy of the harmonics in a vibrating string not infinitesimal?

First of all, one should notice that the dichotomy "eigenmode $-$ non-eigenmode" is a false one. The correct statement is that any generic motion of the string can be decomposed into ...
John's user avatar
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13 votes
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Pressure standing wave nodes at the end of the open side of a tube

From the Wikipedia article on sound: In physics, sound is a vibration that propagates as a typically audible mechanical wave of pressure and displacement. To fully understand how is air ...
dahemar's user avatar
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11 votes

Why do higher harmonics have a lower amplitude than the fundamental frequency?

A simple answer: the total energy of the vibration has to be finite. Given that we have an infinite number of possible modes of vibration (not only harmonics, but let's start with them), you need some ...
fraxinus's user avatar
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11 votes
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Why does plucking a string produce harmonics instead of a pulse?

It does produce a pulse. However, the speed of sound in a string is very large so the pulse reaches the ends of the string very quickly. This means that in a second many reflections occur and you only ...
Miguel Correia's user avatar
10 votes

How are overtones produced by plucking a string?

Eigenmodes of a string have sinusoidal spatial form $f_m(x) = C_m \sin(\pi m x/L)$, where $x$ is the parallel coordinate and $L$ is the length of the string. Plucking a string at a fixed location $x_0$...
Maxim Umansky's user avatar
10 votes
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What do I hear when listening to a computer-generated sine wave?

To generate harmonics, you need a nonlinear element. Loudspeakers are not perfectly linear, so yes, they generate weak harmonics. Air is generally very close to a linear medium for sound unless the ...
John Doty's user avatar
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10 votes

Feynman claimed "The ear is not very sensitive to the relative phases of the harmonics." Is that true?

No. You just found a special case where the relatives phases of all the harmonics adds up into such a big difference in the waveform that you actually can hear it. I expect it works if the fundamental ...
mmesser314's user avatar
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9 votes
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How is it possible that multiple overtones can exist at the same time?

Your mistake is in your initial assumption: When one pulls a string, it starts to oscillate and forms a standing wave with frequency $$f=f_0$$ The only way this is true is if you could start the ...
BioPhysicist's user avatar
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9 votes

If all harmonics are generated by plucking, how does a guitar string produce a pure frequency sound?

For an ideal string, the key point is that all the harmonics are "harmonic" : their frequency is a integer multiple of the frequency of the fundamental. So the movement of the string is periodic and ...
Vincent Fraticelli's user avatar
9 votes

Feynman claimed "The ear is not very sensitive to the relative phases of the harmonics." Is that true?

The way hearing works is that acoustic vibrations that reach you inner ear cause mechanical vibrations of the so-called hair cells inside cochlea. Different hair cells happen to have different sizes ...
John's user avatar
  • 3,772
8 votes

What is fundamental frequency, how does it make sense?

Isn’t frequency how many cycles are completed per second, and isn’t the fundamental frequency only half a cycle When a string, fixed a both ends, vibrates in the fundamental mode, the perpendicular ...
Alfred Centauri's user avatar
8 votes
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Is being "stationary" also an example of a "periodic motion"?

A function $f(t)$ is said to be periodic with period $T$ if the following holds for all $t$: $$ f(t)=f(t+T). $$ As such, the constant function is clearly periodic and every real number is a period. ...
jacob1729's user avatar
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7 votes

Why do higher harmonics have a lower amplitude than the fundamental frequency?

As is often the case in physics, when the properties of string vibration are described invariably the string is treated as an idealized string. Among these idealizations: the string is treated as ...
Cleonis's user avatar
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6 votes

Pressure standing wave nodes at the end of the open side of a tube

You're wondering why pressure nodes form at an open end of a tube. The answer is, they don't! It's just a reasonably good approximation. Physically, consider the air molecules at the center of the ...
knzhou's user avatar
  • 103k
6 votes

Is being "stationary" also an example of a "periodic motion"?

You can say what you like, depending on how you define your terms. For example, you can say that a body at rest is "in motion" with speed $v=0$, but in most circumstances this would not be a ...
Andrew Steane's user avatar
6 votes

Why does plucking a string produce harmonics instead of a pulse?

It does, there are some great high-speed videos on the web of exactly this taking place when a stretched bass guitar string is violently plucked by a heavy-metal musician. Note that the reason that a ...
niels nielsen's user avatar
6 votes

What do I hear when listening to a computer-generated sine wave?

TL;DR As a pure answer to your question, I would say yes, the medium does introduce harmonics, but they are of negligible energy compared to the distortion induced by other pieces of the chain. You'...
ZaellixA's user avatar
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6 votes

How to create a standing wave that doesn't oscillate with the fundamental frequency?

Shortening the string is one way to make it vibrate at a frequency different from the fundamental frequency of the whole string - this is how the high of the tone is change when playing string ...
Roger V.'s user avatar
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5 votes

What is fundamental frequency, how does it make sense?

A standing wave on a string can be thought of as a traveling wave that is bouncing back & forth in one dimension. Every time it reaches one of the ends, it is reflected, either inverted or ...
Michael Seifert's user avatar
5 votes

How are overtones produced by plucking a string?

You start with a triangular form, which has its fourier series. Let's say the initial shape is $f(x)$: $$f(x)=\sum_n a_n \sin \frac{\pi n x}{L}$$ where $n$ counts the modes ($1$ is fundamental). So ...
orion's user avatar
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5 votes

How is it possible that multiple overtones can exist at the same time?

If there are overtones, then the "wave" is not just of the main frequency, but is more complicated. In the linear approximation the tone and overtones may come together - in a superposition, due to ...
Vladimir Kalitvianski's user avatar
5 votes
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Is the first harmonic the prevalent frequency?

It depends on how you pluck the string. Typically when we pluck a string the string immediately before release looks something like this (I've exaggerated the vertical scale for clarity): When you ...
John Rennie's user avatar
5 votes

Why do higher harmonics have a lower amplitude than the fundamental frequency?

As a musician, the answer seems obvious. I can observe it when I play a guitar. When you pluck an open string, the total displacement looks like this. When you pluck a second harmonic with equal ...
chasly - supports Monica's user avatar

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