Audio Filters: Understanding sound waves – Part 1
By Diksha

Audio electronics is a sector that refers to the circuit design that
converts sound into electrical signals or electrical signals back into
sound. Together, several circuits form an audio system. 

An audio system has several functions and, typically, can:

Receive audio signals (via a microphone)
Record and save audio
Transmit audio (through wired or wireless communication channels)
Reproduce audio signals (via speakers)

The audio circuits are what perform the signal processing for the sound in
the form of electrical signals. These circuits can also manipulate the
electrical (audio) signals, such as through filtering, mixing, amplifying,
or reproducing sound from the signals. Such processes are performed by
different circuits or devices.

In this series, we’ll design three audio circuits as follows: 


 Audio crossover
 Audio equalizer
 Audio mixer




Audio Crossover
The audio crossover and equalizer are two different types of audio filters,
which are one of the basic building blocks of an audio system.

Typical audio system 
	
Block Diagram of an Audio System

Before discussing the building blocks of an audio system, it’s important
to understand the physics behind the sound. After all, the circuits designed
for this project technically manipulate electrical signals to represent the
audio. 



Sound as waves
A sound is a form of energy, much like heat, light, and electricity are
forms of energy. Sounds are produced, propagated, and detected as
vibrations. As such, it follows that for the production of sound waves, a
source is required to produce the vibration. Once produced, a vibration will
disrupt any particles that are present in the surrounding environment —
and these particles further disrupt any others that are nearby.

It might be easier to visualize these vibrations as a wave. An analog wave
is produced by the compression and rarefaction of the particles.
Technically, it’s this compression and rarefaction that creates a pressure
wave, which is the sound. In other words, a sound is a pressure wave
that’s characterized by the properties of a waveform-like amplitude,
frequency, and time period.



Sound as a pressure wave

	
Image Showing Sound as Pressure Waves

A sense of hearing is the ability to detect and recognize sound waves. The
perception of sound by humans and animals is determined by the range of
frequencies to which they’re attuned to. Every living creature has a
different sound perception. For example, humans can hear sound frequencies
in the range of 20 Hz to 20 kHz.



Sound pressure level
The physical properties of sound are quantified by a sound pressure level.
It’s the measure of sound pressure in reference to the minimum level that
humans can hear. Sound pressure is expressed as micropascals (µPa) or
pascal (Pa), whereas the sound pressure level is expressed as decibels (dB).



Sound pressure
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 audible by humans is 20 µPa and the
maximum sound pressure perceivable by humans (which is also referred to as
the pain threshold) is 20 Pa.

The sound pressure level is generally expressed in Db and is calculated as
follows:

Lp = 10log(P2/P2ref)

Where…

Lp= sound pressure level
P = sound pressure (Pa)
Pref = reference sound pressure, 20 micro Pa

The reception of sound waves by human ears
	
Image showing Reception of Sound by Human Ears by Pressure Level



Characteristics of a sound wave
A sound wave has three basic properties:
Pitch
Loudness
Tone



1. Pitch
The pitch is the individual perception of sound, which cannot be measured by
any mathematical equation. Rather, it’s determined by how fast a sound
wave is causing air particles to vibrate. It’s expressed as the frequency
of a sound wave and represented by the compression and rarefaction of air
particles. So, the frequency of a pressure wave physically represents how
fast the compression and rarefaction of these particles are happening. 

Although a pitch is typically described by the frequency of a specific sound
wave, it’s not directly related to the frequency. The frequency is simply
the physical property of the audio vibration that’s used to figure out the
pitch of a sound.

The frequency of a wave can be determined by this equation:

    Frequency = 1/Time

Frequency and the time period of a wave have an inverse relationship. For
instance, as the time period goes up, the frequency goes down and vice
versa.

This means the frequency of the sound wave indirectly expresses its pitch.
Frequency is the number of waves in a given time period. The period can be
one second, a minute, or an hour.

The standard (ISI) unit of frequency is Hertz (Hz). The Hertz is defined as
the number of cycles per second. If there are 50 cycles in one second, for
example, the frequency is 50 Hz.  

As human can hear sounds from 20 Hz to 20 kHz, this frequency spectrum is
divided into different frequency bands:  

	Sub-bass: 20  to 60 Hz 
Bass: 60 to 250 Hz
Low mid-range: 250 to 500 Hz
Mid-range: 500 to 2 kHz
Upper mid-range: 2 to 4 kHz
Presence: 4 to 6 kHz
Brilliance: 6 to 20 kHz

A high-frequency wave has a higher pitch and a low-frequency wave has a
lower pitch. Consider the sound of birds chirping (high pitch) compared to
the sound of a dog barking (low pitch).

The sound frequency of a pitch

	
Image Representing Pitch as Sound Frequency



2. Loudness
Loudness is the auditory sensation that refers to the order of a sound wave
from low to loud. Loudness is the property of the sound waves and it’s
related to its amplitude. The higher is the amplitude, the louder the sound
and vice-versa.

The amplitude of a sound wave is set by the vibration of the source. The
source transfers the energy to a medium through vibration. A greater
energetic vibration generates a larger amplitude. 

Loudness represented by the amplitude of a sound wave
	
Image Showing Loudness Represented by Amplitude of Sound Wave

For humans, the loudness of a sound also depends on the sensitivity of their
ears. As humans are sensitive to certain frequencies, loudness depends on
the sound wave amplitude and the frequency within a perceived audio
perception range.

The energy of a sound wave is proportional to the square of the amplitude.
So, the greater the amplitude, the louder the sound and the more energy it
carries. 

Depiction of loudness based on the amplitudes of sound waves
	
Image Showing Loudness of Sound Waves Represented by their Amplitudes



3. Quality
A pure tone is the sound generated by only one frequency. 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 an entire wave vibrates.

Frequency notes, which are a perfect integer multiple of a fundamental note,
are called overtones or harmonics. The sound wave is a combination of
fundamental notes and harmonics. 

The presence of overtones or harmonics distorts a sound and its perception,
and this is referred to as harmonics distortion. The fundamental note and
the harmonics have different amplitudes and energy levels. The lower the
amplitude of harmonics, and the lower the energy of all the harmonics
combined, the greater is the quality of the sound.

Therefore, the amplitude or energy of the harmonics frequencies — such as
2fo, 3fo, 4fo, etc. — compared to the energy of the fundamental frequency,
determines the quality of the sound wave. 

In the next tutorial, we cover acoustic waves, which are a type of sound
wave.