Sound intensity

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