Questions tagged [harmonics]

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27
votes
7answers
4k views

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

When we pluck a string, it vibrates in all possible modes of vibrations. The lowest frequency possible is the fundamental frequency and it is the most significant part of sound. But why do the ...
20
votes
4answers
3k views

How are overtones produced by plucking a string?

I read the following from wikipedia: When a string is plucked normally, the ear tends to hear the fundamental frequency most prominently, but the overall sound is also colored by the presence ...
14
votes
5answers
11k views

Why do harmonics occur when you pluck a string?

When you energise a taut string, the following resonant modes of vibration occur: Plotting on the frequency domain, you can see their corresponding frequencies: But what is the underlying physical ...
13
votes
3answers
13k views

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

I do not understand why standing sound waves can be formed in a one-side or two-side open tube. Consider a one-side open tube. In particular how does the reflection of the wave at the open end occur? ...
10
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2answers
3k views

How can you make harmonics on a string? [duplicate]

For an oscillating string that is clamped at both ends (I am thinking of a guitar string specifically) there will be a standing wave with specific nodes and anti-nodes at defined $x$ positions. I ...
9
votes
4answers
3k views

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

A guitar is a plucked instrument and it is played by plucking a string at an off-centre point fixed at two ends. In general, Fourier analysis tells that all harmonics (the resonant frequencies of the ...
9
votes
3answers
930 views

Need mathematical explanation for different musical notes sound different on different instruments

I am not expert in music. There are number of musical instruments. One (especially a person who knows about music) can blindly recognize which instrument is being played just by listening to it. I ...
9
votes
3answers
1k views

What is fundamental frequency, how does it make sense?

I’m currently going through harmonics, and I do not at all understand the fundamental frequency. I understand that it is the simplest vibration of a string, but I don't understand how can it have ...
7
votes
3answers
13k views

Why are the closed and open ends of an organ pipe nodes and anti-nodes?

Here is a diagram of a wave in an organ pipe you'll find in most physics books Waves in air are longitudinal (not traversal), so what do the curves represent? Why are the open ends always anti nodes ...
7
votes
2answers
112 views

Why coupled oscillators tend to seek integer frequency ratios?

In this document, the author writes (page 225) Coupled oscillators have a tendency to seek frequency ratios which can be expressed as rational numbers with small numerators and denominators. For ...
6
votes
2answers
852 views

Is the usually taught solution to forced harmonic motion just a special solution?

Let's say we have a mass on a spring being driven by a forcing function. Given hook's law, $F = -kx$, and a forcing function of $$F(t) = F_0\sin(\omega t) .$$ We can write: $$ m\frac{d^2x}{dt^2} = -...
6
votes
4answers
21k views

Using $\sin()$ or $\cos()$ for computing SHM?

In simple harmonic motion, you can use either the sin or cos form of the equation but my question is which one do you use when and why? I am having a tough time understanding this, so any help would ...
6
votes
4answers
9k views

Physics of guitar strings

Guitarists normally press down hard on the frets and then pluck a string to obtain a note. However, one can also create notes by just touching the string above a particular fret and plucking. For ...
6
votes
1answer
556 views

Fractional harmonics in musical Instruments

I recently did some Fourier transforms on different audio files containing saxophone or trumpet (John Coltrane/Clifford Brown). I found that with the saxophone, the frequency spectrum occasionally ...
5
votes
3answers
800 views

Physics of a guitar

I understand that when you pluck a guitar string, then a bunch of harmonic frequencies are produced rather than just the frequency of the desired note. If this is true, why does C2 sound so different ...
5
votes
3answers
462 views

Unwanted frequencies in sawtooth tone

Since 440 represents an A note, a 55 Hz tone also represents an A, since it is at 1/8 the frequency. However, when I generate this note in Audacity, I always get unwanted frequencies appearing as ...
5
votes
1answer
80 views

Are there physics, theories that predict standing wave harmonic deviations in curved tubes?

For cylinders, it's widely documented how to predict the harmonic frequencies given the length of the tube, the end conditions and the speed of sound which is in turn determined by what gas is in the ...
5
votes
1answer
10k views

Why do higher pitches appear to be louder?

It may just be in a few cases, but in the case of a flute, a higher pitch appears to come with a perceived higher volume. Is this simply because you need to put more energy into the flute to get a ...
5
votes
2answers
255 views

If photon-photon interactions are impossible, how are higher harmonics generated?

In nonlinear optics, it is a rather common process to use nonlinear materials to produce higher harmonics of an incident wave. About the mechanism of the generation of such higher harmonics, it is ...
5
votes
1answer
840 views

Boundary conditions from single-valuedness of spherical wavefunctions

This question is a follow-up to David Bar Moshe's answer to my earlier question on the Aharonov-Bohm effect and flux-quantization. What I forgot was that it is not the wavefunction that must be ...
4
votes
2answers
192 views

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

I was wondering how it is possible for overtones to co-exist at the same time. When one pulls a string, it starts to oscillate and forms a standing wave with frequency $$f_0 = f$$ Additionally, ...
4
votes
3answers
495 views

Can a standing wave form on a string with both end open

I am fascinated with an idea of an standing wave forming on a string with both end open. If we assume two identical waves coming in of an infinitely long string then for a short period of time, they ...
4
votes
1answer
169 views

Why are there no even harmonics in a closed pipe?

I have seen a diagram on sites such as hyperphysics.com that show that there is a missing bit every time so that it makes every harmonic odd. I was hoping I could get a more intuitive explanation. We ...
4
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1answer
476 views

Significance of higher harmonics

I am analyzing a noise signal and have identified the fundamental frequency of a tone and it's higher harmonics. Say for example given the signal below, The fundamental frequency has a sound pressure ...
4
votes
3answers
127 views

Why, in an open or half-open pipe, must an open end of a standing sound wave have a pressure of zero?

I believe this question was asked in some form before, but I'm not clear on the answer. If a sound wave must equal air pressure when it exits a tube, why is it possible that at many points after the ...
4
votes
1answer
119 views

Calculating the decay rates for modes of an ideal circular membrane (ie. drum head) using wave equations?

I am attempting to solve for the theoretical decay rates of the various (m,n) modes of an ideal circular membrane, if that membrane is excited momentarily by an impulse or deformation. I would ...
4
votes
1answer
6k views

How does a side branch intake resonator (Helmholtz?) work?

This is a generalization of this question, I'm hoping to get some more detailed physics-based info with some math. The intake tube on my car has what I believe to be (I've been trying to research it) ...
4
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0answers
820 views

What is the mechanism of subharmonic oscillations?

It's clear to me from linear systems theory that energy manifested within a fundamental mode of resonance can saturate with the excess energy spilling over into harmonic frequencies greater than the ...
3
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3answers
2k views

Where are the harmonics in the radio spectrum?

When I strike a string on my guitar and look at the audio spectrum, I can see the fundamental frequency as a large peak. I can also see the harmonic frequencies as a train of little peaks at ...
3
votes
3answers
918 views

Harmonic frequencies of a guitar string

I'm studying harmonic frequency at the moment but I'm just a bit confused about something. How are more than one different frequencies able to be produced from plucking a guitar string (fundamental ...
3
votes
4answers
1k views

Simple harmonic motion versus oscillations

I want to see whether certain oscillations in my daily life, such as the oscillation of violin strings when plucked, are simple harmonic motion or not. Can we identify whether an oscillation is simple ...
3
votes
3answers
9k views

Difference between note and tone: which one has only one frequency? [closed]

What is note and tone both in physics and musical terms? Are the two used in different ways in the different fields or are they the same thing. Moreover, which one has only one frequency? Well this ...
3
votes
2answers
190 views

Why can an inner product of an eigenvector also be used as an eigenvector?

In quote box below, there is an inner product of an angular momentum eigenvector. Why can you use this inner product as a new eigenvector for the next part of the work? And why do they "of course" ...
3
votes
4answers
278 views

If a guitar note is determined by the fundamental frequency, what is the relationship between this and octaves?

All the research I've been doing tells me that a guitar note is determined by the fundamental frequency played. But say you play an A on the open A string (110 Hz), and then play a higher octave A by ...
3
votes
1answer
65 views

How can a 2.1 Hz excitation induce resonant vibrations in a structure with a fundamental frequency at 6.3 Hz?

I've come across an example given in a footfall design guide wherein it's mentioned that a floor with a fundamental frequency of 6.3 Hz can be excited to resonance by a person walking at 2.1 Hz ...
3
votes
3answers
384 views

Are square wave harmonics real-life phenomena or just mathematical abstractions?

Based on my limited knowledge, it is my understanding that square waves can be mathematically broken down into an infinite sum of sinusoidal waves (of different amplitudes, frequency, etc) . This is ...
3
votes
2answers
3k views

How to find the first-harmonic frequency from the frequency spectrum of a recording of this harmonic being struck on a guitar?

Just as the title implies, I was trying to find the fundamental frequency of a guitar string at various tensions as a part of an experiment to find its Young's modulus. In the experiment, I connected ...
3
votes
3answers
3k views

Why does an octave on a piano have the divisions of 8 white keys and 5 black keys?

An octave corresponds to a doubling or halving of the frequency. Each octave on a piano and in classical music score is broken downs into 8 white keys and 5 black keys. Is there a physics explanation ...
3
votes
2answers
679 views

How can Hilbert spaces be used to study the harmonics of vibrating strings?

The overtones of a vibrating string. These are eigenfunctions of an associated Sturm–Liouville problem. The eigenvalues 1,1/2,1/3,… form the (musical) harmonic series. How can Hilbert spaces be ...
3
votes
1answer
597 views

Where exactly is the antinode of an air column with open-closed boundary conditions?

Suppose that I have an air column with closed-open boundary condition. The air pressure at the open end of the tube is constrained to match the atmospheric pressure of the surrounding air. Therefore,...
2
votes
3answers
101 views

Relation between frequencies of different harmonies

I know the relation between frequencies of different harmonies is $$ f_n = n\times f_1 $$ but I'm heving trouble to develope the equation which proves this equality. can anyone please give me a lead ...
2
votes
3answers
2k views

Fluid filled harmonic oscillator

A vessel (preferably circular) filled with water is accelerating unidirectionally such that the level of water is higher on one end than the other. What I want to know is that if the vessel is ...
2
votes
2answers
267 views

At what frequency does a string vibrate?

When a string with fixed ends vibrates (e.g. plucking a guitar string) Fourier Theorem says that the vibration can be expressed as a sum of its normal modes, which are sinusoidal vibrations with ...
2
votes
1answer
3k views

Why is the damping force acting on an oscillating system opposite in direction to velocity and not acceleration?

So far I know that the damping force is a frictional force that opposes motion and so it acts in the opposite direction to velocity . Bit why can't the same be said for acceleration doesn't the ...
2
votes
2answers
66 views

Why are there these other “harmonics” (violin-specific terminology) in violins?

I've often read explanations of how standing waves form on the string of a violin and their harmonics but there is another phenomenon I've never seen explained: When you play certain notes, musicians ...
2
votes
1answer
5k views

Harmonics in an open organ pipe

How to solve the following question? An open organ pipe has two adjacent natural frequencies of 500 and 600 Hz. Assume the speed of sound in the air 340m/s. The length of the organ pipe is? What is ...
2
votes
1answer
363 views

Where do pure tones occur in nature, besides harmonics?

When you sound a tuning fork, you hear an pure tone/sine wave of usually 440Hz. Yesterday, I tried hitting a table knife made entirely from stainless steel against a grapefruit. When I held it up to ...
2
votes
2answers
88 views

What is the cause and meaning of harmonics?

Let's suppose that a cantilever is vibrating at a frequency of 2Hz. That means that it goes up and it comes down twice per second. I don't understand what the term harmonic means. I can't grasp how ...
2
votes
1answer
400 views

In which-pattern does the individual-particles move in a longitudinal wave?

Transverse waves, such as upper-surface of pond-water, or in shaking-rope; the Transverse-Wave can be easily understood and drawn (for different times such as at t second, t + 0.25 second, t+0.5 ...
2
votes
1answer
211 views

What is the relationship between harmonic motion and the harmonics of a wave?

I learned about harmonic motion and harmonic oscillators a long time ago in physics, but I can't remember what the relationship between that and and the definition of harmonic in a wave. A harmonic ...