Sound Intensity and Log Manipulation

[Gundam00]

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The humming sound of the traffic light is loud and clear once the car comes to a stop. If you detect its level to be 20 dB, what is its intensity?

So you have to know the constant but how do you solve for I in this case?

 

[Zaids37]

I would also like to know the answer to this question. From what I can gather though...

The threshold intensity (I naught) is equal to 10^-12.

The equation is: B=10log(I/I naught). So basically every change in power deviating from 10^-12 by one degree (one exponent) is a change of 10dB. Since you have 20dB that indicates a change of two degrees on the exponent so it should be 10^-10 as its intensity....I think. I'd like someone else's input to help better explain it to both of us but I could be wrong.

 

[KevinGnapoor]

Pretty certain this is:

dB = 10 log I / Io
20 = 10 log I / Io
2 = log I / Io
10^2 = I / Io => 100
I don't think you need to use the Io in this case because that's just the reference intensity.

 

[Zaids37]

Pretty certain this is:

dB = 10 log I / Io
20 = 10 log I / Io
2 = log I / Io
10^2 = I / Io => 100
I don't think you need to use the Io in this case because that's just the reference intensity.

So its intensity would be 100? Or would it be 100 times the Io intensity...making it 10^-10?

 

[KevinGnapoor]

I = 100 seems logical to me. If the traffic is loud, 10^-10 seems like a low intensity? Also, from the problems I've seen so far, it looks like when asked for intensity, they solve for I / Io. But I'm not 100% sure so don't take my word for it. I'll have to read into this more. OP, do you have the answer for this question?

 

[Zaids37]

Im actually very curious now. 10^-10 may not seem loud but compared to the threshold its pretty loud. I just assumed that I/Io=100 is like an equation, so solving for I:

I=100 x Io

Though I could be wrong too. Hope OP comes back to give the answer or someone else can give some input.

 

[Czarcasm]

Decibals is a scale in reference to the minimal threshold intensity humans can hear: 10^-12. So, if we perceive something as 20 dB (and dB = 10 x log(I/Io), that implies the sound we heard is 100x that of the threshold intensity (since log(100) = 2 and 2x10 = 20dB). So the intensity is 100 x Io or 10^-10 W/m2.

Take a look at this comparison chart: https://www.osha.gov/dts/osta/otm/noise/images/common_sounds.gif. So yeah, 10^-10W/m2 does sound very low, so it seems probable that this person was some distance away from the sound source since intensity drops off with distance. So yeah, it might seem unrealistic but regardless, it's nothing we needed to consider to answer this question.