This document defines sound intensity and decibels. It explains that intensity is the rate of energy transfer per unit area, measured in watts per square meter. The range of human hearing spans from 1x10^-12 W/m2 to 1 W/m2. However, decibels provide a more efficient scale since they are logarithmic units that allow comparison to a reference intensity. The document provides formulas to convert between intensity (I) and decibel (dB) measurements.

1. SOUND
INTENSITY
AND DECIBELS

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

3. DEFINING INTENSITY
(FURTHER)
 The rate at which energy changes over time is called
POWER
 Therefore:

𝐸
𝑡
= P I =
𝑃
𝐴

4. DEFINING INTENSITY
(FURTHERER)
 Units of Power = Watts /Units of Area = meters squared
 Therefore: intensity is in units of W/m2

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

11. THANK YOU FOR READING!
AARON REYES
PHYS 101 202

12. WORKS CITED
 http://hyperphysics.phy-astr.gsu.edu/hbase/sound/intens.html
 Physics for Scientists and Engineers: an Interactive Approach:
Revised Custom Volume 1 – PHYS 101. Hawkes, Iqbal, et al.
Toronto, Ontario. 2015. Page 251