IntensityIntensity

Force to PressureForce to Pressure

The pressure wave creates a The pressure wave creates a force on a slice of air.force on a slice of air.• Wave amplitude Wave amplitude ss00

• Pressure amplitude Pressure amplitude pp00

The amplitudes are related The amplitudes are related by frequency and by frequency and wavenumber.wavenumber.

0

20

1

kpx

P

sa

x

P

xA

PA

m

Fa

P +PP

A

x

02

0

kps

magnitudes from harmonic waves

Force and IntensityForce and Intensity

Intensity is the power per Intensity is the power per unit area.unit area.

Pressure is force per area.Pressure is force per area. Expect Expect II = = PvPv

• Use Use vv = = ss00

• Factor of ½ for averageFactor of ½ for average

P +PP

A

x

v

ppsI

2

20

0021

v

pkps

kps

02

00

020

Threshold of HearingThreshold of Hearing

The minimum intensity that The minimum intensity that can be heard by humans is can be heard by humans is 1010-12-12 W/m W/m22..

What is the fractional What is the fractional variation in air pressure?variation in air pressure?

Translate intensity into Translate intensity into pressure.pressure.

Substitute values.Substitute values.• pp00 = 10 = 10-5-5 Pa Pa

Compared to P = 10Compared to P = 1055 Pa this Pa this is one part in 10 billion.is one part in 10 billion.

vIp

v

pI

2

2

0

20

Intensity RatioIntensity Ratio

SoundSound IntensityIntensity Ratio over thresholdRatio over threshold ThresholdThreshold 1010-12-12 W/m W/m22 101000

WhisperWhisper 1010-10-10 W/m W/m22 101022

MosquitoMosquito 1010-8-8 W/m W/m22 101044

TalkingTalking 1010-6-6 W/m W/m22 101066

TrafficTraffic 1010-4-4 W/m W/m22 101088

SubwaySubway1010-2-2 W/m W/m22 10101010

Rock bandRock band 101000 W/m W/m22 10101212

Jet engineJet engine 101011 W/m W/m22 10101313

Logarithmic ScaleLogarithmic Scale

Sound intensity varies over a Sound intensity varies over a huge range.huge range.• 13 orders of magnitude13 orders of magnitude

The exponents are easier to The exponents are easier to keep track of than the keep track of than the values.values.• Logarithm of the ratioLogarithm of the ratio

SoundSound Ratio exponentRatio exponent ThresholdThreshold 00 WhisperWhisper 22 MosquitoMosquito 44 TalkingTalking 66 TrafficTraffic 88 SubwaySubway1010 Rock bandRock band 1212 Jet engineJet engine 1313

DecibelDecibel

The decibel is a unit that The decibel is a unit that measures the intensity ratio.measures the intensity ratio.• Symbol dBSymbol dB

• Exponent times 10Exponent times 10

Each 10 dB is 10 times more Each 10 dB is 10 times more intensity.intensity.

)/(log)dB 10( 010 II

SoundSound dBdB ThresholdThreshold 00 WhisperWhisper 2020 MosquitoMosquito 4040 TalkingTalking 6060 TrafficTraffic 8080 SubwaySubway100100 Rock bandRock band 120120 Jet engineJet engine 130130

Turn it DownTurn it Down

Your younger sibling is Your younger sibling is watching TV, and its watching TV, and its annoying you at 75 dB. You annoying you at 75 dB. You yell and she turns it down to yell and she turns it down to 60 dB.60 dB.

By what factor has the By what factor has the intensity decreased?intensity decreased?

The difference in logarithms The difference in logarithms is the ratio of the valuesis the ratio of the values

Find the difference in dBFind the difference in dB

Solve for the intensitySolve for the intensity

With values With values II22 / / II11 = 0.032 = 0.032

next

)/log(loglog abab

)/(log)dB 10( 1210 II

10/12

1210

10/

)/(log)dB 10(

II

II