2. DEFINING INTENSITY
I =
𝐸
𝐴𝑡
The energy going through some area divided by that area
and some amount of time.
Note: increasing time DOES NOT increase intensity, in
increases the amount of ENERGY
I = Intensity
E = Energy
A = Area
t = Time
5. FORMULA FOR INTENSITY
Sound travels in a SPHERE, and not in a circle.
Formula for the surface area of a sphere is:
4𝜋𝑟2
Therefore: I =
𝑃
4𝜋𝑟2
Surface area of
a sphere with
radius r
6. RANGE OF HEARING
(IN GENERAL)
Pain threshold of hearing: 1 W/m2
Lowest sound humans can hear: 1 x 10-12 W/m2
These sounds are vibrating at less than a width of one
molecule! Wow!
Reference intensity Io
RANGE OF HEARING: 1013Io
7. DECIBELS
The range of 1013Io (10,000,000,000,000) is far too large
to be used efficiently
We use DECIBELS as a more efficient range
Decibels (dB) are units for logarithmic comparisons of
intensity levels(loudness)
8. INTENSITY LEVEL EQUATION
We want to compare a certain intensity (I) to the
faintest sound a human can possibly hear (Io)
𝐼
𝐼 𝑜
this is a dimensionless number
This number is in between the previous given range
of (10,000,000,000,000)
Since the decibel range is a logarithmic scale, we use
log10 on the given number.
9. INTENSITY LEVEL EQUATION
(MORE)
So far: dB = log10( 𝐼
𝐼 𝑜
)
Because they have been dubbed decibels, the
equation needs to multiplied by 10 (dec- stems from
the Greek root, meaning ten)
Now: dB = 10log10[ 𝐈
𝐈 𝐨
]
10. SOLVING FOR INTENSITY (I)
dB = 10log10[
I
Io
]
Need to get rid of the 10 on the right hand term, so:
𝑑𝐵
10
= log10[
I
Io
]
To get rid of the log10 on the right hand side, raise both
sides to the tenth power:
10dB/10 = [
I
Io
]
To isolate for I, multiply both sides by Io:
Io10dB/10 = I
