Extra Credit: Decibels and Half-Lives Decibel Scale: dB = 10 log(I/I/I0), Ia/Ib

Question

Extra Credit: Decibels and Half-Lives Decibel Scale: dB = 10 log(I/I/I0), Ia/Ib = 10 I = sound intensity in watts per square meter dB se decibels dB Sound 0 Hearing threshold 30 Bedroom at night 60 1 meter conversation 90 Subway train 110 Rock band 140 Pain threshold 200 Saturn rocket at close range For Problems #1-05, 1 point each: how much louder is a ... #1. ... rock band than a subway car? 12. ... subway car than a 1-meter conversation? /3. ... rock band than a bedroom at night? #4. ... Saturn rocket than a rock band? /5. ... subway train than hearing threshold?

Explanation / Answer

1)

Ir / Is = 10^(110 - 90)/10
Ir/Is = 10^(20/10) = 10^2 = 100

So, the rock band is 100 times louder than subway train

2)

Is/Im = 10^(90 - 60)/10
Is/Im = 10^3 = 1000

So, the subway train is 1000 times louder than the conversation

3)

Ir/Ib = 10^(110 - 30)/10
Ir/Ib = 10^8

So, the rock band is 10^8 times louder than the bedroom at night

4)

Is/Ir = 10^((200 - 110)/10)
Is/Ir = 10^9

So, the saturn rocket is 10^9 times louder than the rock band

5)

Is/Ih = 10^(90 - 0)/10
Is/Ih = 10^9

So, the subway train is 10^9 times louder than the hearing threshold

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