– The amount of matter present

– Applies to gases (**AIR**), liquids, & solids

– Air has both mass and weight

Weight is a gravitational force

Weight is a force

- Property that enables recovery from distortion of shape or volume (e.g. pinching skin)

– Air – the tendency of air volume to return to its former volume after compression (e.g., syringe)

All bodies remain at rest or in a state of uniform motion unless another force acts in opposition

• Magnitude of inertia is directly proportional to the mass

With every force there must be an equal and opposite reaction force

– Hammer & nail, bat & ball

– Force cannot exist by itself

– elasticity is the reaction force to inertia

– Vibration sustained by opposing forces (i.e., inertia)

– For a period of time vibration continues without reapplication of external force

• When the density of air increases we call that compression

• When the density of air decreases we call that rarefaction

• So, when a sound travels through air there will be alternate regions of compression and rarefaction

• The medium of air is not displaced over a great distance

• The wave of disturbance moves through the medium

characterized by propagation of density changes through an elastic medium

• When we talk about sound we need to consider specific physical quantities such as:

– Mass

– Density

– Force

– Pressure

– Displacement

• There are three basic physical quantities

– Length

– Mass

– Time

• All other physical quantities are derived

– Displacement

– Velocity

– Acceleration

– Force

– Pressure

• Metric: MKS & cgs

– MKS

• Length (m)

• Mass (kg)

• Time (s)

– cgs

• Length (cm)

• Mass (g)

• Time (s)

• English: fps

– Length (ft)

– Mass (lb)

– Time (s)

• A measure of distance: the amount of spatial separation between two points

– How many times a unit (m, cm, ft) is contained in a given distance

• The quantity of matter present

• Defines the magnitude of inertia

• Inertia is proportional to mass

• MKS – kilogram (kg)

• cgs – gram (g)

• fps – pound (lb)

• The quantity of mass defines the amount of inertia

• A quantity expressed in seconds (s), minutes (min), hours (hrs), etc.

• Units of measure:

– MKS – second (s)

– cgs – gram (s)

– fps – pound (s)

• A change in position

• A vector quantity: incorporates both magnitude and direction

– The amount of displacement per unit time, OR

– The time‐rate of displacement

– Also a vector quantity

– Average velocity

• c = derived displacement (x)/time (t)

• Speed is a scalar quantity (i.e., only magnitude)

• s = d/t

Displacement per unit time

• MKS – m/s

• cgs – cm/s

• fps – ft/s, mph, etc.

• The time‐rate change in velocity

• A vector quantity

• Positive vs. negative acceleration (deceleration)

• a = Δc/t = (c2‐c1)/t

• A push or a pull

• The product of mass (m) and acceleration (a)

• F = ma

• Object has mass (inertia), which opposes change in motion: force is applied to overcome inertia

• Consequences of force

– Distortion of matter, and/or

– Acceleration of matter

Units of Measure:

• MKS – newton (N)

– Force required to accelerate a mass of 1 kg from c = 0 m/s to c = 1 m/s in 1 s

• cgs – dyne

– Force required to accelerate mass of 1 g from c = 0 cm/s to c = 1 cm/s in 1 s

• 1 N = 100,000 dynes

Pressure is a force exerted over an hour on the surface of an object

Pressure decreases as the area over which a force is applied increases.

• Force per unit area

• p = F/A

• p = 1 N/ 100 m2 = 0.01 N/m2 Units of Measure

• 1 N = 100,000 dynes

• 1m = 100 cm

• Thus, 1 N/m2 = 100,000 dynes/m2 (m X m) 1 N/m2 = 100,000 dynes/10,000 cm2 (100 cm X 100 cm)

• Thus, 1 N/m2 = 10 dynes/cm2

The Pascal (Pa)

• 1 Pascal (Pa) = 1 N/m2 or 10 dynes/cm2

• Sound energy is transferred through a medium at some rate

• POWER: the rate at which energy is transferred; Energy transferred per unit time

• ENERGY: the capacity to do work, whereas POWER is the rate at which energy is expressed The WATT – 1 WATT = 1 joule/s (MKS):

• Intensity: Energy per second per square meter

• Units of Measure

– Intensity: watt/m2

• Absolute: The intensity is 3.15 X10‐2 watt/m2

• Relative: Level = Ix/Ir

• For each value of Ix, the ratio Ix/Ir (the level) depends on the value of Ir

10-fold change in Ix?

10^-10 to 10^-9

2-fold change in Ix?

2x10^-6 to 4x10^-6

the reference intensity must always be specified

Ir = 10^-12 watts/m²

• Nominal

• Ordinal

• Interval

• Ratio

• Objects are the same or different

• The letter A is different from the letter B

• The numeral (or a symbol that labels something) 1 is different from the numeral 0

• Two things are the same or different and,

• One object has more or less of some quantity than another

• Letters are not numbers: cannot be added

• Numerals are not numbers either: can’t be added

• E.g., doctor using a scale of 0‐10 to indicate degree of improvement in some condition(0 no improvement) and (10 disappearance of the condition)

• Size of the interval between adjacent numbers is known and is constant

• The size of the interval is called the BASE

• Successive units are formed by adding (or subtracting) base to each number

• Because the base is known we can say that one object is a certain number of intervals more or less than another

• One unit on the scale is so many times greater or less than another

• Successive units are formed by multiplying (or dividing) each number by the BASE

• Successive units differ by a constant ratio, which is the BASE

• The numbers on the scale differ by a constant ratio, and

• They can be expressed as the base, 2 in the previous example, raised to progressively higher powers

• 1. Law 1: (X^a)(X^b) = X^a+b

• 2. Law 2: X^a/X^b= X^a-b

• 3. Law 3: (X^a)^b= X^ab

• 1. Law 1: Log ab = Log a + Log b

• 2. Law 2: Log a/b = Log a – Log b

• 3. Law 3: Log a^b = b Log a

• 4. Law 4: Log 1/a = ‐ Log a

• Pressure is force/unit area

• Unit of measure (MKS): 

N/m2 

Pa, where 1 Pa = 1 N/m2  

μPa, where 1 μPa = 1 μN/m2

To derive an appropriate equation, we consider intensity and pressure in relation to impedance of the medium.

• I is proportional p²

• OR, p √I (the square root of I)

• dB IL: Ir = 10^-12 watt/m²

• An intensity of 10^-12 watt/m² creates a pressure in air of 20 (2 X 10¹)µPa

• Therefore, for dB SPL, the reference pressure, pr, is 20 µPa

• pr is 2 X 10¹µPa

dB SPL = 20 log (px/pr)

2-fold change in px?

2x10⁵ to 4x10⁵

10-fold change in px?

Combining Sound Intensities from Independent Sources

Equal Source Intensities

• dB_N = dB_i + 10 log₁₀N_,

i = dB SPL (or dB IL) from one source

N = # of sources combined

Combining Sound Intensities from Independent Sources

Unequal Source Intensities

• Three steps in solution

1. Calculate intensity from each source

2. Add intensities (carefully)

3. Calculate decibels

• One source = 80 dB SPL, and a second source = 83 dB SPL

• dB = 80 Ix = 1 X 10^-4

• dB = 83 Ix = 2 X 10^-4

• Sum of Ix = 3 X 10^-4

• dB = 10 log (3 X 10^-4 /10^-12)

= 10 log (3 X 10⁸)

= 84.8 dB IL (dB SPL)

Sound Source -->Medium-->Receiver

• Periodic

• Aperiodic

• Frequency/Period

• Phase

• Amplitude

• (wavelength)

– How quickly a sine wave

 repeats itself

– Number of cycles

 completed in 1 sec

– Unit: Hertz

f = 1 / T

(f = 1 / Pr)

– How long it takes to complete 1 cycle. – Unit: sec, ms

T = 1 / f

(Pr = 1 / f)

• sec vs. ms

milli = 1/1000

1 ms = 0.001 sec

1 sec = 1000 ms

• milli vs. micro

milli = 1/1000

micro = 1/1,000,000

• Hz vs kHz

kilo = 1000 times

1000 Hz = 1 kHz

2 kHz = 2000 Hz

• Distance traveled during one period

 • Equation:

 λ = s / f

s = speed of sound

f = frequency

• Examples in air (s = 340 m/s)

f = 1100 Hz

• λ = 340/1100 = 0.3m

f = 550 Hz

• λ = 340/550 = 0.6m 

• How big is the displacement, how far did the

vibrating object move?

• Types of amplitude:

Peak

Peak‐to‐Peak (2 x Peak)

RMS amplitude

• RMS = root‐mean‐square

1. square amplitudes

2. compute mean (average)

3. compute square root

• RMS = 0.707A

• Peak Amplitude = 1.414RMS 

• Composed of more than one sine wave

• Harmonic complex

– All sine waves are integer multiples of the lowest frequency

– Terminology:

• f₀, f₁, f₂, f₃, f₄, etc. = harmonics

f₀ and f₁ are the same

sound composed of sine waves at the following frequencies:

125, 250, 375, 500, 625, 750, 875, 1000 Hz

• Speech sounds may be harmonic complexes

Example: Vowel sound might consist of f0 = 200 Hz and 40 harmonics.

– Sounds with very short duration

– AKA click, tone burst, impulse

– Examples: hand clap, gun shot

– Amplitude varies randomly over time

– Example: White noise

– Amplitude variations as a function of time

– Temporal waveform

- time waveform

- x-axis is time

– Amplitude variations as a function of frequency

– Spectral representation/amplitude spectra/power spectra

- x-axis is frequency

• Broadband or white noise

– All frequencies present

– Amplitudes distributed according to a Gaussian (standard bell curve) distribution

– Phase relationship of the components is random

– White noise = Gaussian noise

- white noise is aperiodic

• Noise that has more limited frequency content than white noise

• How do you create narrowband noise?

– Pass white noise through a filter

Characterizing Frequencies:

- what frequencies "pass

- cutoff frequency

- rejecction rate

Top: Low Pass, let low frequencies through

 Top/Middle: High Pass, let high frequencies through

Bottom/Middle: Band Pass

Bottom: Band Reject

• The sum of all the sinusoids present in the

noise

• Energy in any single component of noise must be less than the total power

• Spectrum level is the average power in 1‐Hz band of the noise

• N₀ = spectrum level

• OAL = overall level of noise (total power) in dB

• BW = bandwidth of noise in Hz

• N₀ = OAL – 10 log BW