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

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

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.