 # Audio and Acoustics Theory

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Audio and Acoustics Theory
Sound Ranges of Hearing Frequency / Wavelength / Period / Speed

What You Need to Learn Today
What sound is and how it travels The frequency range (Hz) and dynamic range (dB) of human hearing How to calculate frequency, wavelength, period and speed of sound

Acoustics: the physics of sound
Psychoacoustics: the human perception of sound

Sound is Vibrations When an object vibrates it causes nearby molecules to vibrate causing a chain reaction Sound energy is the energy produced by sound vibrations as they travel through a specific medium. Sound vibrations cause waves of pressure which lead to some level of compression and rarefaction in the mediums through which the sound waves travel. The study of sound and vibration are closely related. Sound, or "pressure waves", are generated by vibrating structures (e.g. vocal cords); these pressure waves can also induce the vibration of structures (e.g. ear drum). Hence, when trying to reduce noise it is often a problem in trying to reduce vibration. Sound travels through air because air is made of molecules (molecules carry the sound waves by bumping into each other) Electromagnetic waves (light)don’t need molecules to travel; they form when an electric field couples with a magnetic field.

Compressing and rarefacting air molecules

Sound is Vibrations Sound travels as a series of compressions and rarefactions through a medium

Sound is a Mechanical Wave
Sound travels through air as a longitudinal wave However it can also travel as a transverse wave (such as on a guitar string or a wave in water)

Units of frequency, logarithmic progression of musical scales.

1 cycle per second = 1cps = 1 Hertz = 1Hz
One complete cycle is one compression and one rarefaction 1 cycle per second = 1cps = 1 Hertz = 1Hz

Frequency range of hearing
The human ear is capable of hearing frequencies between 20 and 20,000 cycles per second (20Hz to 20kHz)

Frequency range of hearing
20Hz 40Hz 80Hz 100Hz 150Hz 200Hz 10kHz 15kHz 16kHz 17kHz 18kHz 19kHz

Dynamic Range of Hearing
The typically accepted amplitude range of human hearing is 120dBSPL Sound amplitude is referenced to the Pascal (Pa) (the unit for pressure) 0dBSPL = Pascals (20 µPa) 120dBSPL = 20 Pascals The pascal (Pa) or kilopascal (kPa) as a uit of pressure measurement is widely used throughout the world and has largely replaced the pounds per square inch (psi) unit. Standard car tyres are usually best at 36 Psi which is 248 kPa Sound pressure or acoustic pressure is the local pressure deviation from the ambient (average, or equilibrium) atmospheric pressure caused by a sound wave. Sound pressure in air can be measured using a microphone, and in water using a hydrophone. The SI unit for sound pressure p is the pascal (symbol: Pa).

Dynamic Range of Hearing
The pascal (Pa) or kilopascal (kPa) as a uit of pressure measurement is widely used throughout the world and has largely replaced the pounds per square inch (psi) unit. Standard car tyres are usually best at 36 Psi which is 248 kPa Sound pressure or acoustic pressure is the local pressure deviation from the ambient (average, or equilibrium) atmospheric pressure caused by a sound wave. Sound pressure in air can be measured using a microphone, and in water using a hydrophone. The SI unit for sound pressure p is the pascal (symbol: Pa). Decibels relative to full scale, commonly abbreviated dBFS, measures decibel amplitude levels in digital systems such as pulse-code modulation (PCM) which have a defined maximum available peak level. 0 dBFS is assigned to the maximum possible digital level. For example, a signal that reaches 50% of the maximum level at any point would reach -6 dBFS at that point, 6 dB below full scale. Conventions differ for RMS measurements, but all peak measurements will be negative numbers, unless they reach the maximum digital value. 60 decibels of amplitude -60dBFS to 0dBFS

Sine Wave The sine wave is a pure tone with no harmonics. It is a ‘simple waveform’ 1kHz sine wave

Other Simple Waveforms
Sine Square Triangle Sawtooth

HIGHER FREQUENCY LOWER FREQUENCY
shorter wavelength LOWER FREQUENCY longer wavelength

Characteristics of Waveforms
Frequency (number of cycles per second) Wavelength (length of one cycle in metres) Amplitude (strength or power of the wave) Period (time for one cycle in seconds)

Units of Measurement = period of one cycle (in seconds)
= velocity of sound (in metres per second) = wavelength (in metres) = frequency in Hertz (Hertz is cycles per second) = period of one cycle (in seconds)

Velocity of Sound Formula
The velocity of sound through air at 20 degrees Celsius is 344m/s

Wavelength (m) = speed of sound / frequency (Hz)
What is the wavelength of 20Hz? Wavelength (m) = speed of sound / frequency (Hz) = 344 / 20 = 17.2 metres

f = 344 / 0.0172 f = 20,000Hz What frequency has a wavelength
of 1.72cm? Frequency (Hz) = speed of sound / wavelength (m) f = 344 / f = 20,000Hz

What frequency has a period of 2 milliseconds?
frequency in Hz = 1 / period (in seconds) f = 1/.002 f = 500Hz Frequency and period are distinctly different, yet related, quantities. Frequency refers to how often something happens. Period refers to the time it takes something to happen. ms = millisecds. There are 1000ms in 1 second

T = 1/200 T = 0.005 seconds T = 5 milliseconds
What period has a frequency of 200Hz? Answer in milliseconds. period in seconds = 1 / frequency (Hz) T = 1/200 T = seconds T = 5 milliseconds Frequency and period are distinctly different, yet related, quantities. Frequency refers to how often something happens. Period refers to the time it takes something to happen.

What is the speed of sound at 1,263,719°C?
v = (0.6 x 1,263,719) v = 758,562.8 m/s Frequency and period are distinctly different, yet related, quantities. Frequency refers to how often something happens. Period refers to the time it takes something to happen.

The Sound Barrier

The Sound Barrier

Velocity of Sound in Various Mediums
Air > 344 m/s Hydrogen > 1284 m/s Water > 1482 m/s Human Brain > 1540 m/s Gold > 2000 m/s Steel > 5200 m/s Diamond > m/s Human brain is 77 – 78% water It can be anywhere between 3000 m/s and 6000 m/s depending on the type of steel and the direction of propagation of the sound wave

Speed of Sound Through Air
Calculate the speed of sound at: 0°C 5°C 10°C 20°C 30°C v = (0.6xC)

Answers 0°C = 331.4 m/s 5°C = 334.4 m/s 10°C = 337.4 m/s

What are the frequencies of the following wavelengths?
3.4m 5m 50cm 80cm Freq = vel/wavelength

Answers 3.4m = 101 Hz 5m = 68.8 Hz 50cm = 688 Hz 80cm = 430 Hz

Calculate the Wavelength of:
140Hz in air (at 344m/s) 400Hz in steel (at 5000m/s) 500Hz for an electrical signal in wire (at 300,000km/s) Answers: Wavelengths in air at 140Hz = 2.46 metres Wavelengths in steel at 400Hz = 12.5 metres Wavelength in wire at 300,000 km/s = 600 metres

Range of Hearing The ‘accepted’ range of hearing of a young undamaged ear is 20Hz to 20kHz The typical amplitude range is 120dBSPL

Dogs 40 Hz to 60,000 Hz Bats 20 Hz and 120,000 Hz Mice 1 kHz to 70 kHz

In 1876, at the age of 29, Alexander Graham Bell invented his telephone. In 1877, he formed the Bell Telephone Company

The Decibel The Bel is named after Alexander Graham Bell 1847 –1922. The decibel (dB) is a tenth of a Bel In audio, amplitude is measured in decibels A decibel, or its abbreviation dB is a measurement of loudness that ranges from the threshold of hearing, 0dB to the threshold of pain, about 140dB. The term decibel is actually two words: deci, meaning one-tenth, and bel, named after Alexander Graham Bell, the inventor of the telephone, which is why the 'B' is always written in upper case as in dB. So, a decibel is actually one-tenth of a unit of sound measurement known as a bel.

Loudness is Subjective Amplitude is Objective
A decibel, or its abbreviation dB is a measurement of loudness that ranges from the threshold of hearing, 0dB to the threshold of pain, about 140dB. The term decibel is actually two words: deci, meaning one-tenth, and bel, named after Alexander Graham Bell, the inventor of the telephone, which is why the 'B' is always written in upper case as in dB. So, a decibel is actually one-tenth of a unit of sound measurement known as a bel.

Loudness is measured in Phons
Loudness is a subjective term describing the strength of our perception of sound. A decibel, or its abbreviation dB is a measurement of loudness that ranges from the threshold of hearing, 0dB to the threshold of pain, about 140dB. The term decibel is actually two words: deci, meaning one-tenth, and bel, named after Alexander Graham Bell, the inventor of the telephone, which is why the 'B' is always written in upper case as in dB. So, a decibel is actually one-tenth of a unit of sound measurement known as a bel. Loudness is measured in Phons

Threshold of hearing is
Threshold of Pain 120dB Threshold of hearing is A decibel, or its abbreviation dB is a measurement of loudness that ranges from the threshold of hearing, 0dB to the threshold of pain, about 140dB. The term decibel is actually two words: deci, meaning one-tenth, and bel, named after Alexander Graham Bell, the inventor of the telephone, which is why the 'B' is always written in upper case as in dB. So, a decibel is actually one-tenth of a unit of sound measurement known as a bel. 41

To Recap Sound is audible pressure variations which travel as a series of compressions and rarefaction through a medium. Sound is a mechanical wave which is transmitted as longitudinal and transverse waves.

Audio Engineering Society

Papers related to NIHL on AES website
Hearing Loss from Noise and Music Sound Pressure Levels in Symphony Orchestras and Hearing    How the Ear Works and Why Loud Sounds Cause Hearing Loss Preventing Hearing Loss Investigation of the Loud Music Exposure Hearing Loss

Moodle Key to enrol in Trimester 1 classes
amplitude

Next Week Wave Interaction Beat Frequencies Phase Concepts Comb Filtering Waveforms Noise