lecture11_12

lecture11_12 - Definition Logarithms a b = c b = log a c 10...

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Logarithms = c a b c b a log = = c b 10 c c b log log 10 = = Definition: Properties: Numbers: 3 1000 log 1 10 log 845 . 0 7 log 477 . 0 3 log 301 . 0 2 log 0 1 log = = = = = = 0 100 200 300 400 500 600 700 800 900 1000 -0.5 0 0.5 1 1.5 2 2.5 3 x log(x) ( 29 A n A B A B A B A AB n log log log log / log log log log = - = + =

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Sound intensity and power A w I = Intensity: w – power (do not confuse with work) E - energy t - time 2 1 r I 2 2 2 1 1 2 r r I I = Free field (radiation is uniform in all directions): 2 4 r w A w I π = = r - radius of the sphere Power: t E w = I - intensity A - surface area Units: [ ] [ ] [ ] 2 m W I W s J w J E = = = = joul: watt:
Intensity level of sound in decibels: ( 29 0 log 10 I I dB L I = 2 12 0 / 10 m W I - = Decibels ( 29 0 0 log 10 w w dB L L w w = - Power level difference in decibels: Power level in decibels: ( 29 0 log 10 w w dB L w = 0 0 = w L W w 12 0 10 - = 0 0 = I L 10 0 10 I L I I = Doubling intensity increases intensity level by 3 If radiation is equal in all directions, then doubling distance decreases intensity 4 times and decreases intensity level by 6 3 2 log 10

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Example: A source of 500 Hz sound is operated at a power 300 microwatts. The sound radiates with equal intensity in all directions.
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lecture11_12 - Definition Logarithms a b = c b = log a c 10...

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