Understanding Sound and Hearing: Amplitude, Frequency, and Decibels, Slides of Advanced Physics

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Sound and Hearing

Nature of the Sound Stimulus

“Sound” is the rhythmic compression and decompression of the air around us caused by a vibrating object.

The “decibel” (dB)

The decibel is a logarithmic unit used to describe a ratio (i.e., log (x/y)) In engineering analyses, it is used to normalize “power” measurements to a known reference and then compresses the resulting ratio using a log 10 operation. This format is convenient for engineering analyses involving wide dynamic ranges (when very small and the very large magnitudes must be considered simultaneously).

dB = 10 log(Observed Power / Reference)

dB

SPL

The transducers (microphones) on sound level meters measure sound pressure (i.e., N/m 2 or Pascals). Pressure needs to be converted to power prior to calculation of the decibel equivalent….i.e., acoustic power = pressure 2 Finally, we need to agree upon a Reference value. By convention, we use 20 microPa (i.e., the hearing threshold) Thus: dB = 10 log (Observed Pressure 2 / 20 microPa 2 ) However……..

Some Typical Sound Amplitude Values

More about those pesky decibels

• JND for sound intensity is about 1 dB SPL for most of normal range of hearing
• What does 0 dB SPL mean? Hint: 20 log (20 microPa/20 microPA) = 0 dB SPL
• If one machine emits 80 dB SPL then how much sound amplitude would be expected from two machines side-by-side? 2 x 80 = 160 dB SPL ??? (That’s pretty intense) Convert from dB SPL back to raw pressure, sum the pressures, then convert sum to dB SPL 80 dB SPL  antiLog(80/20)  10, 20 log (10,000+10,000) = 86 dB SPL (approx.)

A “Better” Sound Amplitude Table?

130 Loud hand clapping at 1 m distance 110 Siren at 10 m distance 95 Hand (circular) power saw at 1 m 80 Very loud expressway traffic at 25 m 60 Lawn mower at 10 m 50 Refrigerator at 1 m 40 Talking; Talk radio level at 2 m 35 Very quiet room fan at low speed at 1 m 25 Normal breathing at 1 m 0 Absolute threshold dBSPL

Most Sound Stimuli are Complex

Speed of Sound

Acoustic energy results from a traveling wave of rhythmic “compression” through a physical medium (e.g., air; water; steel). It is the “compression” that travels not the medium, per se. The characteristic speed of this travelling wave varies as a function of the medium (elasticity; density). The speed of acoustic energy through the air (aka “sound”) is 331 m/sec (or 742 MPH ) at 0-deg C (Faster at higher temperatures).

Gross Anatomy of the Ear

The “Impedance Problem”

99.9% of sound energy in the air is reflected at the air:water boundary (10 log(0.1/100)) = - 30 dB loss ) (1/1000x) How does the ear compensate for this loss as sound energy is transmitted from the air to the fluid that filled the cochlea? 2 dB gain via ossicular leverage (1.6x) 25 dB gain via surface area condensation (eardrum  stapes) (316x) ~5 dB gain at mid-frequencies (3x) due to pinna and auditory canal resonance

The Cochlea

Photomicrograph: Sensory Hair Cells

Three rows of Outer Hair Cells One Row of Inner Hair Cells

Auditory Transduction