Meaning of the word "Harmonic" in different contexts

Click For Summary
SUMMARY

The term "harmonic" encompasses multiple definitions across various fields, primarily in mathematics and physics. A harmonic function is defined as one that satisfies Laplace's equation, while sine and cosine functions are classified as harmonic in the context of vibrations, despite not solving Laplace's equation. Additionally, terms like "harmonics" and "harmonic oscillators" refer to higher frequencies and repeating motions, respectively. The discussion highlights the complexity and contextual variability of the term "harmonic," suggesting a common etymology linked to stringed instruments.

PREREQUISITES
  • Understanding of Laplace's equation in mathematics
  • Familiarity with harmonic functions and their properties
  • Basic knowledge of vibrations and oscillatory motion
  • Awareness of the concept of overloading notation in mathematics
NEXT STEPS
  • Research the properties of harmonic functions in relation to Laplace's equation
  • Explore the concept of harmonic oscillators in physics
  • Study the harmonic series in music theory and its mathematical implications
  • Investigate the implications of overloading notation in mathematical contexts
USEFUL FOR

Mathematicians, physicists, educators, and students seeking clarity on the term "harmonic" across different disciplines.

JTC
Messages
100
Reaction score
6
A harmonic function is one that satisfies Laplace's equation -- a definition cannot be more precise than that.

However, in the study of vibrations, sine and cosine are considered harmonic functions; but they don't solve Laplace's equation.

And then there are words like: harmonics (for higher frequencies) or "harmonic oscillators" that repeat their motion.

Could someone provide a suite of definitions of the word harmonic?

At the moment, I am confused and thinking that the functions that solve Laplace are related to harmonic oscillators. Am I dealing with multiple definitions?
 
Physics news on Phys.org
JTC said:
Am I dealing with multiple definitions?
Probably. It's an unfortunate and confusing fact of life that many words have different meanings or definitions in different contexts.
 
I'd guess that harmonic in each case may have a common etymology from stringed instruments.

The wikipedia article here makes the connection between the harmonic series in music, harmonic mean, harmonic oscillators, etc. I don't know about the Laplace's equation piece of it though.
 
jtbell said:
Probably. It's an unfortunate and confusing fact of life that many words have different meanings or definitions in different contexts.
Talk aboutthe use of the term " Normal" in Mathematics: https://en.wikipedia.org/wiki/Normal#Mathematics

Talk about overloading notation.
 

Similar threads

How to set up this problem with driven torsional oscillator?
  • · Replies 5 ·
Replies
5
Views
1K
Undergrad Physical Meaning of Atomic Oscillations
  • · Replies 11 ·
Replies
11
Views
2K
Show that the real part of a certain complex function is harmonic
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Are harmonics "real" in a vibrating string?
  • · Replies 58 ·
2
Replies
58
Views
8K
Undergrad Atoms in a harmonic oscillator and number states
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Is the ground state energy of a quantum field actually zero?
  • · Replies 113 ·
4
Replies
113
Views
13K
Undergrad Can the Schrodinger equation satisfy Laplace's equation?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Where is Laplace's Equation Valid in Different Domains?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Using Complex Numbers to find the solutions (simple Q.)
  • · Replies 3 ·
Replies
3
Views
2K
Harmonic Load in the Time and Frequency Domains
  • · Replies 4 ·
Replies
4
Views
2K