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.