What is the difference between note, tone and mode? In physics, wave mechanics and vibration specifically, do the terms note, tone and mode mean the same thing or do they refer to difference things?
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Specifically in relation to music, the terms note, tone and mode of vibration are related but distinct concepts.
1. Musical note:
Each musical note is defined (among other things) by the fundamental frequency of the note. The note $A$ for example has a fundamental frequency of $440\:\mathrm{Hz}$.
2. Tone of a note:
For most instruments the fundamental frequency is far from the only one present in a note's audio spectrum. Usually the fundamental frequency $f_1$ is accompanied by multiples of itself, called harmonics: $f_2=2f_1$, $f_3=3f_1$, $f_4=4f_1,...,f_n=nf_1$ etc. With each harmonic is associated an amplitude $a_i$ so that the full audio spectrum of the note can be represented as:
$$\displaystyle \sum_{n=1}^{+\infty}a_if_i$$
The spectrum of these various $a_i$ gives a musical note its particular tone, timbre (or 'colour').
3. Modes of vibration:
In some cases different modes of vibration are possible; see for example the two main modes of a tuning fork or the vibration modes of a vibrating membrane (a drum membrane).
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$\begingroup$ What is meant by mode of oscillation? $\endgroup$– MrAPCommented Sep 26, 2016 at 16:32
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$\begingroup$ @MrAP: Hi! Did you follow the links? 'Oscillation' is really a sysnonym for vibration. I've edited it now. $\endgroup$– GertCommented Sep 26, 2016 at 17:42
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$\begingroup$ Ya i did but could not understand anything since i do not have that much of a mathematical background. I was asking for a simple description of mode of oscillation. $\endgroup$– MrAPCommented Sep 26, 2016 at 17:45
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$\begingroup$ Look at the tuning fork link and scroll down for a schematic of normal v clanging modes of vibration, for instance. $\endgroup$– GertCommented Sep 26, 2016 at 17:50
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