1. 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).

2. Section 12-1: Characteristics of Sound
Sound: Longitudinal mechanical wave in medium
Source: A vibrating object (like a drum head).

3. 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!

4. Speed of Sound 10

5. 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

6. Example 12-2

7. Sound waves can be considered pressure waves:

8. 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

9. Human Ear: Can detect sounds of intensity: 10-12 W/m2  I  1 W/m2
“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

10. 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  W/m2

11. Loudness of sound, intensity I (in decibels):
β  10 log10(I/I0), I0  1.0  W/m2
For example the loudness of a sound with intensity I = 1.0  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

12. Loudness Intensity

13. 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.

14. Frequencies for
musical notes

15. 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

16. 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.

17. Guitar & all stringed instruments have sounding boards or boxes to amplify the sound!
Examples
12-7 & 12-8

18. 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!

19. Standing Waves: Open-Open Tubes

20. Standing Waves: Open-Closed Tubes

21. 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.

22. 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.