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Loudness

Loudness. October 17, 2007. Loudness. What is it??. The Process. Sound !. At the Eardrum. Pressure wave arrives at the eardrum It exerts a force The drum moves so that WORK IS DONE The Sound Wave delivers ENERGY to the EARDRUM at a measurable RATE.

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Loudness

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  1. Loudness October 17, 2007

  2. Loudness What is it??

  3. The Process Sound !

  4. At the Eardrum • Pressure wave arrives at the eardrum • It exerts a force • The drum moves so that WORK IS DONE • The Sound Wave delivers ENERGY to the EARDRUM at a measurable RATE. • We call the RATE of Energy delivery a new quantity: POWER

  5. Quickie Review • Work = force x distance = energy • Unit is either Joules or KWH (later) • Energy is a good thing. • Wasting energy is bad

  6. POWER Example: How much energy does a 60 watt light bulb consume in 1 minute?

  7. By the way ….. You BUY KWH from the power company.

  8. We PAY for Kilowatt Hours We PAY for ENERGY!! Not Power

  9. More Stuff on Power 10 Watt 10 Watts = 10 Joules per second. INTENSITY = power/unit area

  10. Intensity Inverse Square Law !

  11. So…. 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)

  12. To the ear …. Area of Sphere =4pr2 =4x3.14 x 50 x 50 = 31400 m2 50m Ear Area = 0.000025 m2 30 watt

  13. Continuing Is this a lot?? Scientific Notation = 2.37 x 10-7 watts

  14. Huh?? Move the decimal point over by 8 places. Scientific Notation = 9.5 x 10-8 Another example: 6,300,000=6.3 x 106 Move decimal point to the RIGHT by 6 places. REFERENCE: See the Appendix in the Johnston Test

  15. Scientific NotationAppendix 2 in Johnston 0.000000095 watts = 9.5 x 10-8 watts

  16. The perception of loudness • The brain is not a “linear animal”. • If the ear hears a sound, it sends a certain “signal” (electrical) to the brain. • The brain determines how loud the music is by the size of this signal. • The range of signals in the brain is limited and it has to go over a huge range of loudness so it has to process the signal to be in a useful range. • It uses something called a logarithm.

  17. Decibels - dB • The decibel (dB) is used to measure sound level, but it is also widely used in electronics, signals and communication. • It is a very important topic for audiophiles. • It is a LOGARITHMIC translation so it does what the brain does.

  18. 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. Decibel (dB) ?

  19. 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!

  20. 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.

  21. An example: • The threshold of pain is 1 w/m2 12 Zeros

  22. Another Example

  23. Look at the dB Column

  24. 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)

  25. Can you Hear Me???

  26. Frequency Dependence

  27. Why all of this stuff??? • We do NOT hear loudness in a linear fashion …. we hear logarithmically • 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

  28. 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. • 100dB = 10-2 w/m2

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

  30. Start at the beginning • 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

  31. Remember the definition

  32. 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!

  33. Let’s YELL!!!!

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