Lecture 18 Sound Levels November 1, 2004

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Whutshappenin? Examinations have been graded and returned. Next exam is in THREE WEEKS!!! Then, only one week of lectures followed by the FINAL EXAMINATION There will be NO make-up exam for the final. The only acceptable reason for missing the exam is that you are dead or almost dead.

SCHEDULE REMAINING ITEM DATE WEIGHT (%) Exam #1 Friday, 9/24 15% Monday, 11/22 OP Questions Daily 25% Final Exam Dec. 6th 30%

More Schedule Week Topic November 1 Loudness, decibels and hearing 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 TIME

Recall ENERGY Same energy (and power) goes through surface (1) as through surface (2) Sphere area increases with r2 (A=4pr2) Power level DECREASES with distance from the source of the sound. Goes as (1/r2)

To the ear …. =3.14 x 50 x 50 = 7850 m2 Area of Sphere =pr2 50m Ear Area = 0.000025 m2 30 watt

Continuing Scientific Notation = 9.5 x 10-8

Huh?? Scientific Notation = 9.5 x 10-8 Move the decimal point over by 8 places. Scientific Notation = 9.5 x 10-8 Another example: 6,326,865=6.3 x 106 Move decimal point to the LEFT by 6 places. REFERENCE: See the Appendix in the Johnston Test and Bolemon, page 17.

Scientific Notation Chapter 1 in Bolemon, Appendix 2 in Johnston 0.000000095 watts = 9.5 x 10-8 watts

Decibels - dB The decibel (dB) is used to measure sound level, but it is also widely used in electronics, signals and communication.

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 logarithm? Bindell’s definition: Take a big number … like 23094800394 Round it to one digit: 20000000000 Count the number of zeros … 10 The log of this number is about equal to the number of zeros … 10. Actual answer is 10.3 Good enough for us!

Back to the definition of dB: 10 log (P2/P1) The dB is proportional to the LOG10 of a ratio of intensities. Let’s take P1=Threshold Level of Hearing which is 10-12 watts/m2 Take P2=P=The power level we are interested in.

An example: The threshold of pain is 1 w/m2

Another Example

Look at the dB Column

DAMAGE TO EAR Continuous 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 Dependence

Why all of this stuff??? We hear Logarithmetically We do NOT hear loudness in a linear fashion …. we hear logarithmetically! Think about one person singing. Add a second person and it gets a louder. Add a third and the addition is not so much. Again …. We hear Logarithmetically

Let’s look at an example. This is Joe the Jackhammerer. He makes a lot of noise. Assume that he makes a noise of 100 dB.

At night he goes to a party with his Jackhammering friends. All Ten of them! How Loud is this "Symphony"?

Start at the beginning 9 6 3 Remember those logarithms? Take the number 1000000=106 The log of this number is the number of zeros or is equal to “6”. Let’s multiply the number by 1000=103 New number = 106 x 103=109 The exponent of these numbers is the log. The log of {A (106)xB(103)}=log A + log B 9 6 3

Remember the definition

Continuing On The power level for a single jackhammer is 10-2 watt. The POWER for 10 of them is 10 x 10-2 = 10-1 watts. A 10% increase in dB!

Let’s think about sizes of things. Music is primarily between 50 and 5000 Hz. Look at the table:

v=344 m/s 0.688 frequency wavelength size 50 6.88 100 3.44 200 1.72   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

E A R Helmholtz Resonartor

C R O S - E T I N

The Ear Spread Out Fluid

The Cochlea

The Cochlea Unwound

The Cochlea Schematic Rubber Membrane Frequency Info Low Frequency High Frequency

Resonance in the Basilar Membrane (Computed)

The Hair Cells

Simplified Version Resonance !!

Damage from very LOUD noises. Extreme Acoustic Trauma Guinea Pig Stereocilia damage (120 dB sound) Control, not exposed After Exposure

The Overall Hearing Process Sound is created at the source. It travels through the air. It is collected by various parts of the ear (semi-resonance). The tympanic membrane moves with the pressure variations. The inner ear filters/amplifies the sound.

Hearing Continued The sound hits the membrane at the entrance to the cochlea. The pressure on the basilar membrane causes it to mive up and down. The resonant frequency of the membrane varies with position so that for each frequency only one place on the membrane is resonating.

Some more on hearing There are hair cells along the basilar membrane which move with the membrane. The motion of the hair cells creates an electrical (ionic) disturbance which is wired to the brain. The disturbance is in the form of pulses. The brain somehow relates the number of pulse firings per second to tone and .. Wallah … music!

Next Stop – Room Acoustics