Quantifying Sound Level

Physical definition of sound

Sound is an organized movement of molecules caused by a vibrating body in some medium - water, air, rock, or whatever

Perceptual definition of sound

Sound is the auditory sensation produced through the ear by the alteration… in pressure, particle displacement, or particle velocity which is propagated in an elastic medium

What two things do you need to create a sound?

A vibrating source and a transmitting medium

What two properties are needed to vibrate an object?

Mass (inertia) and elasticity (restoring force) (virtually every object has both)

A transmitting medium needs to have what properties?

Mass (inertia) and elasticity (restoring force)

Why does the vibratory motion occur?

Due to the oposing forces of inertia and elasticity

Newton’s first law of motion

Inertia: An object will either stay moving or stay still

Newton’s third law of motion

Reaction forces:

-Every force has an equal and opposite reaction force

-Elasticity is the “reaction force” to inertia

Sound waves

a pattern of vibratory motion in the surrounding medium created by the vibrations of a sound source

Wave

A disturbance of variation which travels through a medium

Air as a sound medium

• The air mass surrounding us is made up of 100’s of billions of air molecules per cubic inch

  • Results in pressure of ~15 pounds/inch² (100,000 Pascals (Newtons/Meter²))

• These molecules are constantly moving

  • ~940 mph— referred to as the Brownian Motion

Sound waves in the air

-Vibratory “patterns” are transmitted through the medium at the “speed of sound”

• each molecule “vibrates in place” so actual molecule displacement is small

• The results in alternating areas of compression and rarefaction

  • The amount of compression and rarefaction is related to the original displacement

Compression

increase in air pressure/density of the air mass

Rarefaction

decrease in pressure/density of the air mass

Simple sounds

-Puretones (sinusoids) are the only “simple” sounds

• Vibratory pattern results in smooth regular oscillations

• AKA simple harmonic or sinusoidal motion

-Rare/not real in nature but easy to describe

Complex sounds

Everything else! anything not puretone/sinusoidal

Acoustic or sound power

The rate sound energy travels through a medium

-measured in Watts

• or Joules/second

• Not used much in audiology

-calculated, not measured directly

Sound intensity

The acoustic or sound power per unit area

• Measured in Watts/m²

• Has a level and direction

• If we know sound intensity, we can calculate sound power

Sound pressure

The force of a sound on a surface area perpendicular to the direction of the sound

-Measured in Pascals (Newtons/m²) or dynes/cm²

-Routinely measured in audiology with a sound level meter (but levels are reported in decibels)

-A pattern of pressure changes

• Sound level meters measure changes in air pressure

• Atmospheric pressure is large but changes in sound pressure in the air that we hear are very small

Sound intensity (I) is proportional to what?

-The square of sound pressure (p²)

The problem with sound levels in Pascals

-In Pascals the range of levels relevant to hearing is huge! The range is too large and hearing is much more specific

-.0002 Pascals ——→ 20 Sound pressure level in Decibels

What is the Decibel

-A relative measure that makes a large range of absolute values more manageable

-The dB uses log values (exponents) to compress the large pressure variations in Pascals into a smaller range

-Logs compress the range of 1-10,000 down to a range of 0-4

Logarithm

The exponent of a base number

-Log of 1 = 0 (10^0 = 1)

• 1 Pascal = 10^0 Pascals

-Log 10,000 = 4 (10^4 = 10,000)

• 10,000 Pascals = 10^4 Pascals

The decibel is the…

Log of a ratio of pressure changes

What does hearing sounds depend on?

detecting changes in sound pressure

P1

Actual sound pressure change

P2

Reference sound pressure change (could be any number but must be specified)

What do we use for sound pressure level (SPL) measures

We multiply the log of the ratio by 20 to “expand” our range a bit

-decibel (in SPL) = 20 * log(p1/p2)

3 steps to converting a sound pressure (pascals or dynes/cm²) into a decibel value

1. Take a ratio of two pressure (P actual/P reference)

2. Take the log of the ratio to compress the range of ratios

3. Expand the range some by multiplying by 20

dB is simply a…..

Ratio

Sound pressure level (dB SPL)

Means the reference pressure level (p2) is 20 micropascals (or .0002 dynes/cm²)

Practical reasons for using the Decibel

-Linear scale is cumbersome and hard to compare individual thresholds

-Comparing threshold shifts is not intuitive

Theoretical reasons for using the Decibel

-Auditory system appears to compress the loudness of sounds in a similar way. For example:

• Sound pressure of .2 Pascals is 100 times larger than a sound pressure of .0002 Pascals

• But a .2 Pascal sound (80 dB SPL) is NOT perceived as 100 times louder than a .0002 Pascal sound (40 dB SPL)

  • It is closer to ~16 times as loud

How do we measure sound levels?

We use a “sound level meter” (SLM) to measure sound pressure changes in the air. Measures the sound level in the free field

What if you want to know the level of a sound delivered to the ear by an earphone?

Put a microphone in the person’s ear or use a coupler