Wave

Sound move in the form of longitudinal wave.  Analysis of this waveform is complex.  A simpler visualization is to use a transverse wave.  When throwing a rock into water, it creates ripples.  When looked at from above, the ripples propagate outwards in the form of longitudinal wave.  When looked at form the side (like a cross section), we see the transverse waveform.  The upper part of a transverse wave represents the greatest point of compression, while the lowest point represents the rarefaction.  The mid point is the position of molecule which it is not vibrating, is called the standard reference level.

A sinusoidal wave represents simple harmonic motion (SHM).  A sine waveform result from mass vibration is the simplest and most economical way because it only contains a single frequency and has no harmonic content.  Otherwise, the wave is called a complex periodic waveform.  A waveform without pattern is called a random waveforms.

Frequency = speed of sound/wave length

The range of frequency human can hear is between 20 to 20kHz.  Sound below the lower limit of hearing is called subsonic, whereas above the limit is called ultrasonic.  Cat can hear between 45Hz to 85kHz.  Bat and dolphin can hear up to 120kHz.

Music occupies about 1/4 of the range of hearing.  The fundamental tone in music is that which you hear most prominently when an instrument is played.  It occupies about 50% of the total sound heard.  Some example of the frequency range of musical instruments:

violin = 200Hz to 3.5kHz
viola = 124Hz to 1kHz
Cello = 63Hz to 630Jz
Double Bass = 40Hz to 200Hz
Guitar = 80Hz to 630Hz
Piano = 28Hz to 4.1kHz

When hearing a periodic wave, we are actually hearing a complex averaging of the waveform's peak to peak values.  The root mean square (RMS) ks the average level of a waveform over time.  For a sine wave, RMS = 0.707*peak values.

Unlike frequency, amplitude cannot be measured without a reference value.  Decibel is a logarithmic unit representing a ratio.  Intensity level of a sound is measured as the energy transmitted per unit time and area of a sound wave.  The greater the amplitude of a vibration, the greater the energy transmitted.

I = P/S of which P = Power (energy) and S = area covered

The loudest sound one hear is about 1 W/m2, which is a trillion times more energy than the softest sound (1*10-12 W/m2).  These values are very awkward to use and so decibels are used.  Another reason is that we hear sound intensity logarithmically.

Decibel is one tenth of a Bel (derived from Alexander Graham Bell).  Bel is a ration of 10 to 1 between 2 numbers.  The amount of energy between 1 Bel and 2 Bel is 10 times.  The standard ratio of hearing is 0 dB SPL (Sound Pressure Level).  10 dB SPL is 10 times louder than 0 dB SPL.  20 dB is 100 times louder than 0 dB.

When we walk away from a sound, the loudness decrease following the inverse square law.

When 2 sounds of difference frequencies (e.g. 100 Hz and 105 Hz) are produced at the same time, they produce a pulsation effect, call beats.  The number of beats = f1 - f2.  When the difference between 2 frequencies is greater than 30 Hz to 40 H, the beat phenomenons ceases to exists.  In its place is the existence of the simultaneous sounding 2 frequencies known as interval in music.