How are decibels calculated on a logarithmic scale?

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In summary, decibels are a unit of measurement for sound energy and the absolute threshold for hearing is set at zero decibels. Every 10 decibels represents a ten-fold increase in sound, meaning normal conversation at 60 dB is 10,000 times louder than a whisper at 20 dB. The 10 fold system uses a log scale equation, where I(db) = 10*log_{10}(\frac{I}{I_0}), to determine the sound intensity. This means that 10 dB represents a sound intensity of 10, 20 dB represents 100, and 30 dB represents 1000. The number of zeros after the 1 in the decibel value indicates the sound intensity in
  • #1
Genecks
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Decibels are the measuring unit for sound energy. The absolute threshold for hearing is arbitrarily defined as zero decibels. Every 10 decibels correspond to a ten-fold increase in sound. Thus, normal conversation (60 dB) is 10,000 time louder than a 20 dB whisper.

I don't understand the math of the 10 fold system.
Could someone go into detail of it for me?

I just don't see how that works.

10 db = 100
20 = 1000
30 = 10000?

i don't understand the system here.
 
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  • #2
It's a log scale

[tex]
I(db) = 10*log_{10}(\frac{I}{I_0})
[/tex]

For example

[tex]
10db = 10*log_{10}(10)
[/tex]

[tex]
30db = 10*log_{10}(1000)
[/tex]


[tex]
60db = 10*log_{10}(1000000)
[/tex]
 
  • #3
I don't understand that log stuff or I think I'd have this understood by now.

==update==
Ah, I understand it a bit better now after doing some math work. Thank you.

simply the 6 part of 60 could signify 6 zeros after the 1, making it 1 million.
 
Last edited:

1. What is the definition of a decibel?

A decibel is a unit of measurement for the intensity of sound or the power of an electrical signal. It is a logarithmic scale that compares the magnitude of a signal to a reference level.

2. How is the decibel scale used in psychophysics?

In psychophysics, decibels are used to measure the perception of sound loudness or the perception of brightness in visual stimuli. They are used to quantify the relationship between physical stimuli and the human perception of those stimuli.

3. What is the difference between dB SPL and dB HL?

dB SPL (sound pressure level) is a measure of the physical intensity of sound, while dB HL (hearing level) is a measure of the perceived loudness for an individual with normal hearing. dB HL takes into account the varying sensitivity of human hearing at different frequencies.

4. How does the decibel scale relate to the human perception of sound?

The decibel scale is logarithmic, meaning that a change of 10 dB is perceived as a doubling or halving of loudness. This means that small changes in decibel levels can result in significant differences in perceived loudness by humans.

5. What is the threshold of hearing in decibels?

The threshold of hearing is the lowest level of sound that can be detected by the human ear, and it is measured at 0 dB SPL. This is equivalent to the softest sound that a person with normal hearing can perceive.

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