Meaning of the word "Harmonic" in different contexts

In summary, harmonic functions satisfy Laplace's equation and can be seen in the study of vibrations. However, other concepts such as harmonics and harmonic oscillators also involve the term "harmonic" but may not necessarily relate to Laplace's equation. This can lead to confusion and multiple definitions of the word. Similarly, the term "normal" in mathematics can have different meanings depending on the context, highlighting the concept of overloading notation.
  • #1
JTC
100
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?
 
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  • #2
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.
 
  • #3
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.
 
  • #4
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.
 

1. What is the definition of "harmonic" in music?

In music, a harmonic refers to a sound that is produced by a vibrating string or column of air that is a whole-number multiple of the fundamental frequency. It is also used to describe a chord or group of notes that sound pleasing when played together.

2. How is "harmonic" used in physics?

In physics, harmonic refers to a type of motion or oscillation in which there is a regular and repeating pattern. This can be seen in systems such as a pendulum or a mass on a spring, where the motion is back and forth in a predictable manner.

3. What does "harmonic" mean in the context of waves?

In the context of waves, harmonic refers to a wave that has a frequency that is an integer multiple of the fundamental frequency. This means that the wave pattern repeats at regular intervals, creating a harmonic series.

4. How is "harmonic" used in mathematics?

In mathematics, harmonic can refer to several different concepts, including a type of function or equation, a type of sequence, or a type of mean. In general, it is used to describe a relationship or pattern that repeats at regular intervals.

5. Can "harmonic" have different meanings in different contexts?

Yes, the word "harmonic" can have different meanings depending on the context in which it is used. It can refer to a musical concept, a physical phenomenon, a wave pattern, or a mathematical relationship. It is important to consider the context in order to understand the specific meaning of the word in a given situation.

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