Chapter 12: Sound
• A few (selected) topics on sound
• Sound: A special kind of wave.
• Sound waves: Longitudinal mechanical waves in a
medium (not necessarily air!).
– Another definition of sound (relevant to biology): A
physical sensation that stimulates the ears.
• Sound waves:
– Need a source: A vibrating object
– Energy is transferred from source through medium
with longitudinal waves.
– Detected by some detector (could be electronic
detector or ears).
Section 12-1: Characteristics of Sound
• Sound: Longitudinal mechanical wave in medium
– Source: A vibrating object (like a drum head).
• Sound: A longitudinal mechanical wave
traveling in any medium.
• Needs a medium in which to travel!
– Cannot travel in a vacuum.
 Science fiction movies (Star Trek, Star Wars), in
which sounds of battle are heard through vacuum
of space are WRONG!!
• Speed of sound: Depends on the medium!
Speed of Sound
10
• Loudness: Related to sound wave energy (next
section).
• Pitch: Pitch  Frequency (f)
– Human Ear: Responds to frequencies in the range:
20 Hz  f  20,000 Hz
f > 20,000 Hz 
Ultrasonic
f < 20 Hz
 Infrasonic
Example 12-2
• Sound waves can be considered pressure waves:
Section 12-2: Sound Intensity
• Loudness: A sensation, but also related to
sound wave intensity.
• From Ch. 11: Intensity of wave:
I  (Power)/(Area) = P/A (W/m2)
• Also, from Ch. 11: Intensity of spherical wave:
I  (1/r2)

(I2/I1) = (r1)2/(r2)2
• “Loudness” A subjective sensation, but also
made quantitative using sound wave intensity.
• Human Ear: Can detect sounds of intensity:
10-12 W/m2  I  1 W/m2
• Sounds with I > 1 W/m2 are painful!
– Note that the range of I varies over 1012!
“Loudness” increases with I, but is not simply  I
Loudness
• The larger the sound intensity I, the louder the sound.
But a sound 2  as loud requires a 10  increase in I!
– Instead of I, conventional loudness scale uses
log10(I) (logarithm to the base 10)
• Loudness Unit  bel or (1/10) bel  decibel (dB)
• Define: Loudness of sound, intensity I (measured in
decibels):
β  10 log10(I/I0)
I0 = A reference intensity  Minimum intensity
sound a human ear can hear
I0  1.0  10-12 W/m2
• Loudness of sound, intensity I (in decibels):
β  10 log10(I/I0), I0  1.0  10-12 W/m2
– For example the loudness of a sound with intensity
I = 1.0  10-10 W/m2 is:
β = 10 log10(I/I0) = 10 log10(102) = 20 dB
• Quick logarithm review (See Appendix A):
log10(1) = 0, log10(10) = 1, log10(102) = 2
log10(10n) = n, log10(a/b) = log10(a) - log10(b)
• Increase I by a factor of 10:
 Increase loudness β by 10 dB
Loudness Intensity
Section 12-4: Sound Sources
• Source of sound  Any vibrating object!
• Musical instruments: Cause vibrations by
– Blowing, striking, plucking, bowing, …
• These vibrations are standing waves produced
by the source: Vibrations at the natural
(resonant) frequencies.
• Pitch of musical instrument: Determined by
lowest resonant frequency: The fundamental.
• Frequencies for
musical notes
• Recall: Standing waves on strings (instruments):
Only allowed frequencies ( harmonics) are:
fn = (v/λn) = (½)n(v/L)
fn = nf1 , n = 1, 2, 3, …
f1 = (½)(v/L)
 fundamental
Mainly use f1
Change by changing L
(with finger or bow)
Also change by changing tension FT & thus v:
v = [FT/(m/L)]½
• Stringed instruments (standing waves with
nodes at both ends): Fundamental frequency
L = (½)λ1  λ1 = 2L  f1 = (v/λ1) = (½)(v/L)
• Put finger (or bow) on string: Choose L & thus
fundamental f1. Vary L, get different f1.
• Vary tension FT & m/L & get different v:
v = [FT/(m/L)]½ & thus different f1.
• Guitar & all stringed instruments have sounding
boards or boxes to amplify the sound!
• Examples
12-7 & 12-8
• Wind instruments: Use standing waves (in
air) within tubes or pipes.
– Strings: standing waves  Nodes at both
ends.
• Tubes: Similar to strings, but also different!
Closed end of tube must be a node, open
end must be antinode!
Standing Waves: Open-Open Tubes
Standing Waves: Open-Closed Tubes
• Summary: Wind instruments:
• Tube open at both ends: Standing waves:
Pressure nodes (displacement antinodes) both
ends:
• Fundamental frequency & harmonics:
L = (½)λ1  λ1 = 2L  f1 = (v/λ1) = (½)(v/L)
fn = (v/λn) = (½)n(v/L) or
fn = nf1 , n = 1, 2, 3, …
Basically the same as for strings.
• Summary: Wind instruments :
• Tube closed at one end: Standing waves:
Pressure node (displacement antinode) at end.
Pressure antinode (displacement node) at the
other end.
• Fundamental frequency & harmonics:
L = (¼)λ1  λ1 = 4L  f1 = (v/λ1) = (¼)(v/L)
fn = (v/λn) = (¼)n(v/L) or
fn = nf1 , n = 1, 3, 5,… (odd harmonics only!)
Very different than for strings & tubes open at both ends.