Audio Theory
What is Sound? • Transfer of Energy • Molecular Displacement • Wave Energy • Mechanical Wave • Pressure Waves • Longitudinal Pressure Waves
Sound Pressure Waves Longitudinal Wave Transverse Wave • Sound waves in air • Initial wave transmission • Compression • Rarefaction
Sound Radiation • Free-field radiation • The output of a point source radiates in a perfect sphere whose surface area is found by: • S = 4 π r 2 • If we double our distance from a sound source we actually increase the total area that the sound will radiate by 4 times • For each doubling in distance there is a 6 dB decrease in level. • A convenient reference point for acoustic measurement.
Sound Pressure Waves • Periodic Motion • The sine wave • One complete wave sequence is known as a Cycle (360 ˚) • The time interval to complete a cycle is known as the Period(T)
The Sine Wave • Easily Measured and Predictable • Frequency (pitch) • Amplitude (loudness) • etc...
Waveform Characteristics Frequency Amplitude Velocity 7 of them Wavelength Phase Harmonic Content Envelope
Frequency • How often the the pressure oscillation occurs • Expressed in Hertz or cycles per second (cps) • # of cycles / time (sec) = f in Hertz(Hz) • 3cycles/3ms=1kHz or 3/.003 = 1000 Hz • The Period (T) of a wave is the time it takes to pass through 360 degrees (one cycle) • T = 1/f
Frequency • # of divisions x Sec/Div Volts/Div • #cycles/sec = f 0.1 V • 1 cycle = 4ms Sec/Div • f =1/.004=250Hz 2 ms
Frequency • 20Hz - 20kHz - Human range of hearing • Humans are sensitive to Proportional changes • 2 to 1 Ratio = Octave interval • Each doubling provides twice the spectral content of the previous octave • We use a logarithmic scale to describe it
Frequency - Bandwidth • All systems have a finite bandwidth • Human Hearing - 20 Hz to 20 kHz • Electronic Devices - Variable
Frequency • Bandwidth is the range from the lowest to the highest frequencies that are no more than 3dB down. 40 Hz 10 kHz 3 dB dB Bandwidth 20 Hz 20 kHz frequency
Amplitude • Maximum displacement from a reference point • Magnitude of change in oscillaton • Pendulum • Electrical Voltage or Alternating Current (AC)
Amplitude 0.707V -1V +1V 0 Amplitude RMS Peak Peak-to-Peak
Amplitude • Peak • = 1.414 x rms voltage • Peak to Peak • RMS - Root Mean Square • Type of averaging • Square root of the mean over time • = .707 x Peak Voltage +1V 0.707V Peak Peak-to-Peak RMS Amplitude 0 -1V
Amplitude � # of divisions x Volts/Div • Peak V= 1V • Peak to Peak V= 2V Volts/Div 0.5 V • RMS V= .707V Sec/Div 20 µ s
Velocity • Speed at which something travels through a medium • Speed of Sound • Variables • Density • Elasticity • Temperature
Velocity • Speed of sound in air (c) at 70°F (20°C) is: • c = 344 ±0.05 meters/sec • c = 1130 ±0.16 feet/sec • Equations for different temperatures • c = 331 + 0.607*TC (TC = °C) • c = 1052 +1.106*TF (TF = °F) • The rate will increase at a rate of 1.1 ft/sec for each degree Fahrenheit and .607 m/sec for each degree Celsius.
Substance Temp(°C) Speed (m/s) Gasses Carbon Dioxide 0 259 Oxygen 0 316 Air 0 331 Air 20 343 Helium 0 965 Liquids Chloroform 20 1004 Ethanol 20 1162 Mercury 20 1450 Water 20 1482 Solids Lead – 1960 Copper – 5010 Glass – 5640 Steel – 5960 The speed of light in a vacuum is ~ 300,000,000 meters per second The speed of an electromagnetic wave in copper is ~ 90% of the speed of light
Velocity • Sound travels at the speed of the molecules of the medium • All sound waves travel at the same speed, in similar conditions • Frequency and Amplitude change the rate and force at which the molecules move into each other
• Sound = energy transfer through longitudinal compression waves • Period = Time it takes to complete 1 cycle (oscillation) of a wave (T=1/ f) • Frequency = Cycles per second (pitch) • Amplitude = Magnitude of displacement from equilibrium (level or loudness) • Velocity = speed of wave propagation (ft/sec or m/sec)
Wavelength • The measured distance between the beginning and end of a cycle. Velocity • Wavelength = frequency • Acoustical wavelength • λ = c/f • Also stated as • V= ƒ * λ
Same Velocity - Different Wavelength
Same Frequency - Different Velocity
Wavelength • Concert A = 440Hz • At 70º F, what is the length of one cycle 1130 2.56 feet = 440 • Bass Drum = 40Hz • At 70º F, what is the length of one cycle 1130 28.25 feet = 40
Wavelength • Flute (High C) 1130 0.54 feet = • 2093 Hz 2093 6.48 inches • Piccolo (High C) 1130 0.27 feet = • 4186 Hz 4186 3.24 inches
Wavelength affect on Propagation • Wavelength determines how a sound wave will react as it comes into contact with an object in its path • Diffraction • Refraction • Reflection
Wavelength • Diffraction • The bending of waves around obstacles and the spreading out of waves beyond openings. • Interaction dependent on wavelength
Diffraction Long Wavelengths • When the wavelength is longer than the obstacle it acts as if it (the obstacle) isn’t even there
Diffraction • When a wavelength is near to the size of the obstacle both Shadowing and Re-radiation occur • Resonances
Diffraction Short Wavelengths • Wavelength shorter than object in its path • Pronounced Reflection • Very Clear Shadow Zone
Diffraction at Openings • Small Opening = New Source Point • Large Opening = Continued waveform • Slight shadowing
Diffraction
Diffraction Text http://hyperphysics.phy-astr.gsu.edu
Diffraction http://hyperphysics.phy-astr.gsu.edu
Refraction • The bending of a waveform as it passes from one medium to another • Function of speed of sound in medium • Temperature changes affect velocity • Waves bend towards the slower (cooler) side
Refraction
Refraction Cool Air S o u n d Source Warm Air •When the air is cooler above a surface the wave will bend upwards. • When the air is warmer then the surface the wave will bend downwards.
Refraction Inversion
Reflection • Sound waves reflect where angle of incidence is equal to angle of reflection • Except that... • Convex surfaces deflect waves • Concave surfaces focus waves at one point
Reflection
Reflection • Considerations • Reflection will be strong if absorption is low • Phase change upon reflection • Standing waves • If the surface is random, scattering occurs
Wave Interaction • Diffraction, Refraction, Reflection • Interference • Superposition • Constructive • Destructive • Beating • Moving Sources • Doppler Effect • Standing Waves
Interference • When two waves traveling through the same medium collide they pass through each other • Superposition • Constructive Interference • Destructive Interference • Beating • ƒ (beat) = (ƒ1 - ƒ)
Phase and Phase Shift • The measurement of a cycle, in degrees, • Divided into 360°
Phase and Phase Shift • When two waveforms are completely in phase there is 0°phase difference. • 100% coherent • If two waves are completely out of phase (180°) they will completely cancel each other out. • 0% coherent • Wire reversal = electrically out of phase • Acoustic phase cancellation might occur if two microphones receive the same source one with a positive pressure and the other with a negative pressure.
Phase • Sum and Difference • Coherency • Interference • Beating • Alternating constructive/destructive interference • Two waves of near similar frequency combine to produce a new wave • ƒ (beat) = (ƒ1 - ƒ)
Standing Waves • A wave that doesn’t move ??? • Appears static • Two waves • Same Frequency • Same Wavelength • Traveling in the same plane from opposite directions • Nodes • Antinodes
Standing Waves • Reflected energy • Resonance • The essence of tuned instruments
Doppler Effect • Moving sound source • Shift in frequency and wavelength • Speed vs. Frequency • Observed pitch change as sound source moves in relation to listener
Inverse Square Law • If we double our distance from a sound source we actually increase the total area that the sound will radiate by 4 times (in a free field). • 4 π r 2 • For each doubling in distance there is a 6 dB decrease in level. • dB = 20Log d1/d2 • Example: A speaker has a level of 95 dB at 5 ft, What level can we expect at 14 ft? • 20Log 5/14 = -8.9 dB • 95 - 8.9 = 86.1 dB
Harmonics • The world does not exist of pure tones exclusively. • Timbre • Enables us to distinguish between musical instruments • Fundamental • The note being played • Partials or Overtones or Harmonics • Every other frequencies present including the fundamental.
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