Qualities of sound

Whenever we describe a sound as 'audible', what actually matters is how a human listener PERCEIVES it -- a purely subjective response, unlike the wave's own objective, measurable properties. Three subjective qualities of sound matter most: pitch, timbre (quality), and loudness.

1. Pitch. Pitch is the sharpness or shrillness we perceive in a sound, and it tracks the sound's FREQUENCY: raising the frequency raises the perceived pitch (the sound feels 'sharper'). A tone is the term for a single, pure frequency, while a note may be built from one or more than one tone together. We describe a higher-frequency sound as 'high pitch' or 'high tone'. Because pitch/sharpness is fundamentally a SUBJECTIVE sensation, statements like 'a sound of double the frequency is doubly sharp' are meaningless -- pitch does not scale linearly (or in any simple numerical way) with frequency, it is simply perceived as higher. A high-pitched sound also need not be a LOUD one -- pitch and loudness are entirely separate qualities. A guitar's tones are sharper (higher pitch) than a bass guitar's; a tabla's sound is sharper than a dagga's; and, generally, a female voice is sharper than a male voice. In an audio amplifier or equaliser, raising the treble control boosts the higher-frequency (sharper) content, while raising the bass control boosts the lower-frequency content.
2. Timbre (sound quality). This is what lets you instantly recognise a friend's voice on the phone, or tell apart the very same song played on a guitar, a violin, a harmonium and a piano, even though each instrument is producing broadly the same musical NOTE. Timbre depends on the particular MIXTURE of the fundamental tone together with its overtones that any given sound source (including your own vocal organ) produces -- a mixture unique to that source's construction/physiology. Even your own voice's quality differs noticeably between morning and evening, and is drastically altered by a cold or cough. The full concept of overtones (and how they combine to build a given timbre) is developed only in Class XII, once stationary waves have been introduced.
3. Loudness. The measurable, objective quantity behind loudness is a wave's intensity -- proportional to the square of its amplitude, $I\propto A^2$, measured in W/m². Loudness is simply the human PERCEPTION of that intensity: more intensity is perceived as more loudness, but the relationship is NOT linear -- doubling the intensity makes a sound perceptibly louder, but not 'doubly loud'; human hearing (like human vision, for brightness) responds approximately LOGARITHMICALLY to the underlying physical stimulus. Taking the least audible intensity a healthy human ear can detect as the reference $I_0=10^{-12}\ \text{W/m}^2$, the loudness L of a sound of intensity I, in the unit bel, is defined as $L=\log_{10}\left(\dfrac{I}{I_0}\right)\ \text{bel}$. Since 1 decibel (db) = 0.1 bel (exactly as 1 decimetre = 0.1 m), loudness expressed in decibels is simply ten times the value in bel: $L_{db}=10\log_{10}\left(\dfrac{I}{I_0}\right)$. At the reference intensity itself, $I=I_0$, giving $L=0$ db -- the threshold of hearing. At 10 db, $I/I_0=10$; at 20 db, $I/I_0=100$; and so on -- each additional 10 db corresponds to a TEN-FOLD jump in actual intensity, even though it is perceived as only roughly a DOUBLING of loudness (so 40 db sounds about twice as loud as 20 db, even though its intensity is a hundred times greater, and ten-thousand times that of a 10 db sound) -- a striking demonstration of how compressed the logarithmic decibel scale is relative to the underlying physical intensity. …