Lecture 18Lecture 18Sound LevelsSound Levels

November 1, 2004November 1, 2004

Whutshappenin?Whutshappenin? Examinations have been graded and Examinations have been graded and

returned.returned. Next exam is in THREE WEEKS!!!Next exam is in THREE WEEKS!!!

Then, only one week of lectures Then, only one week of lectures followed by the FINAL EXAMINATIONfollowed by the FINAL EXAMINATION– There will be NO make-up exam for the There will be NO make-up exam for the

final.final.– The only acceptable reason for missing the The only acceptable reason for missing the

exam is that you are dead or almost dead.exam is that you are dead or almost dead.

ITEM DATE WEIGHT (%)

Exam #1 Friday, 9/24 15%Exam #2 Friday, 10/22 15%Exam #3 Monday, 11/22 15%

OP Questions Daily 25%Final Exam Dec. 6th 30%

SCHEDULE REMAININGSCHEDULE REMAINING

More ScheduleMore ScheduleWeek Topic

November 1 Loudness, decibels and hearing

November 8 Room Acoustics, Diffraction and Wave interference

November 15 Simple Electricity and Introduction to Speakers and Microphones

November 22 Examination #3, 1 Lecture this week. Continuation of previous.

November 29 Completion of Electrical Aspects of Music (depends on time)

December 6t FINAL EXAM

ENERGY PER UNIT TIMEENERGY PER UNIT TIME

secJoule1 watt 1

SecondJoulesPOWER

TimeUnit Energy

RecallRecall

Same energy (and power) goes through Same energy (and power) goes through surface (1) as through surface (2)surface (1) as through surface (2)

Sphere area increases with rSphere area increases with r22 (A=4 (A=4rr22)) Power level DECREASES with distance Power level DECREASES with distance

from the source of the sound.from the source of the sound.– Goes as (1/rGoes as (1/r22))

ENERGY

To the ear ….To the ear ….

50m

30 watt

Area of Sphere =r2

=3.14 x 50 x 50 = 7850 m2Ear Area = 0.000025 m2

ContinuingContinuing2

2 /004.0785030/ mw

mwattAreaUnitPower

watts.000000095powerEarAt

000025.0m

watt.004

ear Power to

22

m

Scientific Notation = 9.5 x 10-8

Huh??Huh??

Scientific Notation = 9.5 x 10-8

Move the decimal pointover by 8 places.

Another example: 6,326,865=6.3 x 106

Move decimal pointto the LEFT by 6 places.

REFERENCE: See the Appendix in the Johnston Testand Bolemon, page 17.

Scientific NotationScientific NotationChapter 1 in Bolemon, Appendix 2 in JohnstonChapter 1 in Bolemon, Appendix 2 in Johnston

0.000000095 watts = 9.5 x 10-8 watts

Decibels - dBDecibels - dB The decibel (The decibel (dBdB) is used to ) is used to

measure sound level, but it is measure sound level, but it is also widely used in electronics, also widely used in electronics, signals and communication. signals and communication.

Decibel continued (dB)Decibel continued (dB)Suppose we have two loudspeakers, the first playing a sound with power P1, and another playing a louder version of the same sound with power P2, but everything else (how far away, frequency) kept the same.

The difference in decibels between the two is defined to be

10 log (P2/P1) dB       

where the log is to base 10.

?

What the **#& is a What the **#& is a logarithm?logarithm?

Bindell’s definition:Bindell’s definition: Take a big number … like 23094800394Take a big number … like 23094800394 Round it to one digit: 20000000000Round it to one digit: 20000000000 Count the number of zeros … 10Count the number of zeros … 10 The log of this number is about equal to the The log of this number is about equal to the

number of zeros … 10.number of zeros … 10. Actual answer is 10.3Actual answer is 10.3 Good enough for us!Good enough for us!

Back to the definition of dB:Back to the definition of dB:

The dB is proportional to the LOGThe dB is proportional to the LOG1010 of of a ratio of intensities.a ratio of intensities.

Let’s take PLet’s take P11=Threshold Level of =Threshold Level of Hearing which is 10Hearing which is 10-12-12 watts/m watts/m22

Take PTake P22=P=The power level we are =P=The power level we are interested in.interested in.

10 log (P2/P1)

An example:An example: The threshold of pain is 1 w/mThe threshold of pain is 1 w/m22

1201210)10log(1010

1log 10

:PAIN of thresholdfor the rating dB

1212-

Another ExampleAnother Example

01.1010

1100

1:

22

Example

Look at the dB ColumnLook at the dB Column

DAMAGE TO EARDAMAGE TO EARContinuous dB   Permissible Exposure Time      85 dB                           8 hours      88 dB                           4 hours      91 dB                             2 hours      94 dB                             1 hour      97 dB                             30 minutes    100 dB                             15 minutes    103 dB                             7.5 minutes    106 dB                             3.75 min (< 4min)    109 dB                             1.875 min (< 2min)    112 dB                              .9375 min (~1 min)    115 dB                              .46875 min (~30 sec)

Frequency DependenceFrequency Dependence

Why all of this stuff???Why all of this stuff??? We do NOT hear loudness in a linear We do NOT hear loudness in a linear

fashion …. we hear fashion …. we hear logarithmeticallylogarithmetically!!– Think about one person singing.Think about one person singing.– Add a second person and it gets a Add a second person and it gets a

louder.louder.– Add a third and the addition is not so Add a third and the addition is not so

much.much.– Again ….Again ….

Let’s look at an example.Let’s look at an example. This is Joe the This is Joe the

Jackhammerer. Jackhammerer. He makes a lot He makes a lot

of noise.of noise. Assume that he Assume that he

makes a noise makes a noise of 100 dB.of 100 dB.

At night he goes to a party At night he goes to a party with his Jackhammering with his Jackhammering

friends.friends.All Ten of them!

Start at the beginningStart at the beginning Remember those logarithms?Remember those logarithms? Take the number 1000000=10Take the number 1000000=1066

The log of this number is the number of The log of this number is the number of zeros or is equal to “6”.zeros or is equal to “6”.

Let’s multiply the number by 1000=10Let’s multiply the number by 1000=1033

New number = 10New number = 1066 x 10 x 1033=10=1099

The exponent of these numbers is the log.The exponent of these numbers is the log. The log of The log of {{A (10A (1066)xB(10)xB(1033))}}=log A + log B=log A + log B

9 6 3

Remember the definitionRemember the definition

WattP

PPP

P

PP

mwattP

PPdB

2

12

1212

2120

0

10

2)log(20)log(10

120)log(10100)10log(10)log(10100

)10log()log(10)10/log(10100

/10

log10

Continuing OnContinuing On The power level for a single jackhammer is The power level for a single jackhammer is

1010-2-2 watt. watt. The POWER for 10 of them isThe POWER for 10 of them is

– 10 x 1010 x 10-2 -2 = 10= 10-1-1 watts. watts.

110)10log(101010log10 11

12

1

dB

A 10% increase in dB!

Let’s think about sizes of Let’s think about sizes of things.things.

Music is primarily between 50 and Music is primarily between 50 and 5000 Hz.5000 Hz.

Look at the table:Look at the table:

v=344 m/sfrequency wavelength size

50 6.88  

100 3.44  

200 1.72 height or a person

500 0.688  

1000 0.344  head

2000 0.172 <size of head

5000 0.0688 size of pinna

10000 0.0344 ~length of ear canal

EAR

Helmholtz Resonartor

CROSS-SECTION

The Ear Spread OutThe Ear Spread Out

Fluid

The CochleaThe Cochlea

The Cochlea UnwoundThe Cochlea Unwound

The Cochlea SchematicThe Cochlea Schematic

Rubber Membrane

Low Frequency High Frequency

Frequency Info

Resonance in the Basilar Resonance in the Basilar MembraneMembrane(Computed)(Computed)

The Hair CellsThe Hair Cells

Simplified VersionSimplified Version

Resonance !!

Damage from very Damage from very LOUDLOUD noises. noises.

Extreme Acoustic TraumaExtreme Acoustic Trauma

Control, not Control, not exposedexposed

After After ExposureExposure

Guinea Pig StereociliaGuinea Pig Stereocilia damage (120 dB damage (120 dB sound)sound)

The Overall Hearing ProcessThe Overall Hearing Process Sound is created at the source.Sound is created at the source. It travels through the air.It travels through the air. It is collected by various parts of the It is collected by various parts of the

ear (semi-resonance).ear (semi-resonance). The tympanic membrane moves with The tympanic membrane moves with

the pressure variations.the pressure variations. The inner ear filters/amplifies the The inner ear filters/amplifies the

sound.sound.

Hearing ContinuedHearing Continued The sound hits the membrane at the The sound hits the membrane at the

entrance to the cochlea.entrance to the cochlea. The pressure on the basilar membrane The pressure on the basilar membrane

causes it to mive up and down.causes it to mive up and down. The resonant frequency of the The resonant frequency of the

membrane varies with position so that membrane varies with position so that for each frequency only one place on for each frequency only one place on the membrane is resonating. the membrane is resonating.

Some more on hearingSome more on hearing There are hair cells along the basilar There are hair cells along the basilar

membrane which move with the membrane.membrane which move with the membrane. The motion of the hair cells creates an The motion of the hair cells creates an

electrical (ionic) disturbance which is wired electrical (ionic) disturbance which is wired to the brain.to the brain.

The disturbance is in the form of pulses.The disturbance is in the form of pulses. The brain somehow relates the number of The brain somehow relates the number of

pulse firings per second to tone and ..pulse firings per second to tone and .. Wallah … music!Wallah … music!

Next Stop – Room AcousticsNext Stop – Room Acoustics