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Audio Filters - Understanding Sound Waves - 1/8

Written By: 

Diksha
The audio electronics is a branch of electronics that deals with designing of circuits that convert sound into electrical signals or electrical signals back into the sound. These circuits all together form an audio system. 
 
Basically, an audio system is designed to receive audio signals (via microphone), record audio in some storage, transmit audio (through wired or wireless communication channels) and reproduce audio signals (via speakers). So, the audio circuits perform signal processing for representing the sound in the form of electrical signals, manipulate the electrical (audio) signals like amplifying, filtering or mixing, reproduce sound from the audio signals, store audio into computer files or reproduce audio from an audio file. All these processes are performed by different audio related circuits or devices. In this series, three of such audio circuits or devices will be designed. These circuits will be as follow - 
 
1) Audio Crossover
2) Audio Equalizer
3) Audio Mixer
 
The Audio Crossover and Equalizer are two different types of audio filters. The Audio Filters are one of the basic building blocks of an audio system. A general audio system can be represented by the following block diagram - 
 
Block Diagram of an Audio System

Block Diagram of an Audio System

This series will discuss all these building blocks of the audio system followed by the design of circuits for audio  crossover, equalizer and mixer. Before jumping over to the building blocks of an audio system, it is important to understand the physics behind the sound. After all, all the circuits designed in this series are ultimately meant to manipulate electrical signals as representation of it. 
 
Sound as Waves
 
Hearing is one of the five senses. Perhaps, Hearing and Vision are the most important senses in the human world. Hearing is all about detecting and recognizing sound waves. 
 
In terms of physics, sound is also a form of energy as other forms of energy like heat, light and electricity. The sound is produced, propagated and detected in the form of vibrations in the surrounding medium. For the production of sound waves, a source is required which produces the vibration. This vibration disturbs the particles which are present in the surrounding medium and these particles disturb the adjoining particles. Like this, an analog wave is produced in all the directions by the compression and rarefaction of the particles. This compression and rarefaction create a pressure wave which is none other than the sound. So, sound is actually a pressure wave and is characterized by the properties of a waveform like amplitude, frequency and time period. The compression and rarefaction of particles  of the surrounding medium can be graphically represented as follow - 
 
Representation of Sound as Pressure Wave

Representation of Sound as Pressure Wave

The perception of sound by different living creatures is determined by the range of frequencies to which their ears or hearing senses are sensitive to. Every living creature has different sound perception like human ears can hear the sound in a frequency range of 20 Hz to 20 kHz. 
 
Sound Pressure Level- 
 
Now known that sound is a pressure wave, it is important to quantify its physical properties. This quantification of sound is done in terms of Sound Pressure Level (SPL). It is the measure of sound pressure to a reference level or the minimum level that humans can hear. The sound pressure is expressed in terms of uPa or Pa and Sound Pressure Level is expressed in terms of dB (decibel). 
 
Sound pressure –
 
The Sound Pressure is the force (in Newton) on a surface area (m2) perpendicular to the direction of the sound. The Unit of sound pressure is N/m2 or Pa (Pascal). The lowest sound pressure possible by humans to hear is 20 micro Pascal and maximum sound pressure perceivable by humans that is also referred as pain threshold is 20 Pascal. The Sound Pressure Level is generally expressed in Db and is calculated as follow - 
 
Lp = 10log(P2/P2ref)
Where, 
Lp= sound pressure level
P = sound pressure (Pa)
Pref = reference sound pressure, 20 micro Pa
 
Sound Pressure Level

Sound Pressure Level

Characteristics of sound wave
 
In order to recognize distinct sound waves, it is important to understand basic physical properties of the sound. The sound waves have three basic properties which are as follow - 
 
1.Pitch
2.Loudness 
3.Tone
 
Pitch –
 
Pitch is the individual perception of sound, which cannot be measured by any mathematical equation. This is then determined by how fast the sound wave is making the air particles to vibrate. This is expressed as the frequency of sound wave as on graphically representing compression and rarefaction of air particles, the frequency of the pressure wave physically represents how fast the compression and rarefaction of particles is happening. 
Though pitch is generally described by the frequency of the sound wave but it is not directly related to the frequency. The frequency is just the physical property related with the pitch of the sound which can be measured. The frequency of a wave can be determined by the following equation - 
 
Frequency = 1/Time
Frequency and time period of a wave have an inverse relation, as the time period goes high, frequency goes low and vice versa.
 
So indirectly the frequency of the sound wave expresses its pitch. Frequency is the number of waves in a time period. The period can be 1 sec, 1 min or even 1 hour. The standard (ISI) unit of frequency is Hertz. The Hertz is defined as the number of cycles per second. Like if there are 50 cycles in one sec then the frequency is said to be 50 Hertz. Hertz is usually abbreviated as Hz.  
 
As human ears can hear sound from 20 Hz to 20 kHz. This frequency spectrum is divided into different frequency bands which are as follow - 
Sub bass - 20 Hz  to 60 Hz  
Bass - 60 Hz – 250 Hz 
Low Mid Range - 250 Hz to 500 Hz
Mid Range - 500 Hz to 2 kHz 
Upper Mid Range - 2 kHz to 4 kHz 
Presence - 4 kHz to 6 kHz 
Brilliance - 6 kHz to 20 kHz 
 
The high-frequency wave has a higher pitch and low frequency has a lower pitch. For example, the sound of chirping birds has a high pitch as compared to the barking of a dog.
 
Representation of Pitch as Sound Frequency
 

Representation of Pitch as Sound Frequency

 Loudness-
 
Loudness is the auditory sensation which describes the ordering of sound wavefrom low to loud. Loudness is the property of the sound waves which is related to its amplitude. The higher is the amplitude, louder is the sound and vice-versa. The amplitude of the sound wave is set by the vibration of the source. The source transfer the energy to the medium through vibration and more energetic vibration generate larger amplitude. 
 
Amplitude of Sound Wave Representing Loudness

Amplitude of Sound Wave Representing Loudness

The loudness of the sound also depends on the sensitivity of human ears. Human ears are sensitive to some frequencies, so the loudness depends on the sound wave amplitude as well as the frequency that lies in the sensitivity region of human perception.
 
The energy of the wave is proportional to the square of the amplitude. So, more is the amplitude and louder is the sound, more is the energy carried by it. 
 
 Loudness of Sound Waves Represented by their Amplitudes
 Loudness of Sound Waves Represented by their Amplitudes
 
1.Quality –
 
For understanding the quality of the wave it is important to understand about harmonics and the fundamental frequency of the sound.
A pure tone is the sound generated by only one frequency. Like tone generated by the electronic signal generator produces a single frequency sound. In a sound wave there are various tones or notes of frequency but the fundamental note (fo) has the highest amplitude so it can be heard easily. The fundamental note is the frequency at which the entire wave vibrates. The frequency notes which are a perfect integer multiple of fundamental note are called overtones or harmonics. The sound wave is a combination of fundamental notes and harmonics. 
 
The presence of overtones or harmonics distort the sound and its perception. Such kind of distortion is called harmonics distortion. Both the fundamental note and the harmonics have different amplitudes and so the energy levels. Least is the amplitude of harmonics and least is the energy of all the harmonics combined, greater is the quality of sound. So, energy or amplitude of the harmonics frequencies like 2fo, 3fo, 4fo etc. compared to energy of the fundamental frequency fo, determines the Quality of the sound wave. 
 
In the next tutorial, acoustic waves will be discussed. The acoustic waves are just a kind of sound waves.