{"id":1517,"date":"2018-02-06T18:12:53","date_gmt":"2018-02-06T18:12:53","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/suny-osuniversityphysics\/?post_type=chapter&p=1517"},"modified":"2018-02-06T18:12:53","modified_gmt":"2018-02-06T18:12:53","slug":"17-chapter-review","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-osuniversityphysics\/chapter\/17-chapter-review\/","title":{"raw":"17 Chapter Review","rendered":"17 Chapter Review"},"content":{"raw":"
\r\n
\r\n

Key Terms<\/span><\/h3>\r\n
\r\n \t
beat frequency<\/strong><\/dt>\r\n \t
frequency of beats produced by sound waves that differ in frequency<\/dd>\r\n<\/dl>\r\n
\r\n \t
beats<\/strong><\/dt>\r\n \t
constructive and destructive interference of two or more frequencies of sound<\/dd>\r\n<\/dl>\r\n
\r\n \t
bow wake<\/strong><\/dt>\r\n \t
v-shaped disturbance created when the wave source moves faster than the wave propagation speed<\/dd>\r\n<\/dl>\r\n
\r\n \t
Doppler effect<\/strong><\/dt>\r\n \t
alteration in the observed frequency of a sound due to motion of either the source or the observer<\/dd>\r\n<\/dl>\r\n
\r\n \t
Doppler shift<\/strong><\/dt>\r\n \t
actual change in frequency due to relative motion of source and observer<\/dd>\r\n<\/dl>\r\n
\r\n \t
fundamental<\/strong><\/dt>\r\n \t
the lowest-frequency resonance<\/dd>\r\n<\/dl>\r\n
\r\n \t
harmonics<\/strong><\/dt>\r\n \t
the term used to refer collectively to the fundamental and its overtones<\/dd>\r\n<\/dl>\r\n
\r\n \t
hearing<\/strong><\/dt>\r\n \t
perception of sound<\/dd>\r\n<\/dl>\r\n
\r\n \t
loudness<\/strong><\/dt>\r\n \t
perception of sound intensity<\/dd>\r\n<\/dl>\r\n
\r\n \t
notes<\/strong><\/dt>\r\n \t
basic unit of music with specific names, combined to generate tunes<\/dd>\r\n<\/dl>\r\n
\r\n \t
overtones<\/strong><\/dt>\r\n \t
all resonant frequencies higher than the fundamental<\/dd>\r\n<\/dl>\r\n
\r\n \t
phon<\/strong><\/dt>\r\n \t
numerical unit of loudness<\/dd>\r\n<\/dl>\r\n
\r\n \t
pitch<\/strong><\/dt>\r\n \t
perception of the frequency of a sound<\/dd>\r\n<\/dl>\r\n
\r\n \t
shock wave<\/strong><\/dt>\r\n \t
wave front that is produced when a sound source moves faster than the speed of sound<\/dd>\r\n<\/dl>\r\n
\r\n \t
sonic boom<\/strong><\/dt>\r\n \t
loud noise that occurs as a shock wave as it sweeps along the ground<\/dd>\r\n<\/dl>\r\n
\r\n \t
sound<\/strong><\/dt>\r\n \t
traveling pressure wave that may be periodic; the wave can be modeled as a pressure wave or as an oscillation of molecules<\/dd>\r\n<\/dl>\r\n
\r\n \t
sound intensity level<\/strong><\/dt>\r\n \t
unitless quantity telling you the level of the sound relative to a fixed standard<\/dd>\r\n<\/dl>\r\n
\r\n \t
sound pressure level<\/strong><\/dt>\r\n \t
ratio of the pressure amplitude to a reference pressure<\/dd>\r\n<\/dl>\r\n
\r\n \t
timbre<\/strong><\/dt>\r\n \t
number and relative intensity of multiple sound frequencies<\/dd>\r\n<\/dl>\r\n
\r\n \t
transducer<\/strong><\/dt>\r\n \t
device that converts energy of a signal into measurable energy form, for example, a microphone converts sound waves into an electrical signal<\/dd>\r\n<\/dl>\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n

Key Equations<\/span><\/h3>\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Pressure of a sound wave<\/td>\r\n\u0394<\/span>P<\/span>=<\/span>\u0394<\/span>P<\/span>max<\/span><\/span><\/span>sin<\/span>(<\/span>k<\/span>x<\/span>\u2213<\/span>\u03c9<\/span>t<\/span>+<\/span>\u03d5<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u0394P=\u0394Pmaxsin(kx\u2213\u03c9t+\u03d5)<\/span><\/span><\/td>\r\n<\/tr>\r\n
Displacement of the oscillating molecules of a\r\n
<\/div>\r\nsound wave<\/td>\r\n
s<\/span>(<\/span>x<\/span>,<\/span>t<\/span><\/span>)<\/span><\/span>=<\/span>s<\/span>max<\/span><\/span><\/span>cos<\/span>(<\/span>k<\/span>x<\/span>\u2213<\/span>\u03c9<\/span>t<\/span>+<\/span>\u03d5<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>s(x,t)=smaxcos(kx\u2213\u03c9t+\u03d5)<\/span><\/span><\/td>\r\n<\/tr>\r\n
Velocity of a wave<\/td>\r\nv<\/span>=<\/span>f<\/span>\u03bb<\/span><\/span><\/span><\/span><\/span><\/span>v=f\u03bb<\/span><\/span><\/td>\r\n<\/tr>\r\n
Speed of sound in a fluid<\/td>\r\nv<\/span>=<\/span>\u03b2<\/span>\u03c1<\/span><\/span><\/span><\/span>\u203e\u203e\u221a<\/span><\/span><\/span><\/span><\/span><\/span>v=\u03b2\u03c1<\/span><\/span><\/td>\r\n<\/tr>\r\n
Speed of sound in a solid<\/td>\r\nv<\/span>=<\/span>Y<\/span>\u03c1<\/span><\/span><\/span><\/span>\u203e\u203e\u221a<\/span><\/span><\/span><\/span><\/span><\/span>v=Y\u03c1<\/span><\/span><\/td>\r\n<\/tr>\r\n
Speed of sound in an ideal gas<\/td>\r\nv<\/span>=<\/span>\u03b3<\/span>R<\/span>T<\/span><\/span>M<\/span><\/span><\/span><\/span>\u203e\u203e\u203e\u203e\u221a<\/span><\/span><\/span><\/span><\/span><\/span>v=\u03b3RTM<\/span><\/span><\/td>\r\n<\/tr>\r\n
Speed of sound in air as a function of temperature<\/td>\r\nv<\/span>=<\/span>331<\/span>m<\/span>s<\/span><\/span>T<\/span>K<\/span><\/span><\/span>273<\/span><\/span>K<\/span><\/span><\/span><\/span><\/span>\u203e\u203e\u203e\u203e\u203e\u221a<\/span>=<\/span>331<\/span>m<\/span>s<\/span><\/span>1<\/span>+<\/span>T<\/span>C<\/span><\/span><\/span>273<\/span>\u00b0<\/span>C<\/span><\/span><\/span><\/span><\/span>\u203e\u203e\u203e\u203e\u203e\u203e\u203e\u203e\u203e\u221a<\/span><\/span><\/span><\/span><\/span><\/span>v=331msTK273K=331ms1+TC273\u00b0C<\/span><\/span><\/td>\r\n<\/tr>\r\n
Decrease in intensity as a spherical wave expands<\/td>\r\nI<\/span>2<\/span><\/span>=<\/span>I<\/span>1<\/span><\/span>(<\/span>r<\/span>1<\/span><\/span><\/span>r<\/span>2<\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>I2=I1(r1r2)2<\/span><\/span><\/td>\r\n<\/tr>\r\n
Intensity averaged over a period<\/td>\r\nI<\/span>=<\/span>\u2329<\/span>P<\/span>\u232a<\/span><\/span><\/span>A<\/span><\/span><\/span><\/span><\/span><\/span><\/span>I=\u2329\u00a0P\u00a0\u232aA<\/span><\/span><\/td>\r\n<\/tr>\r\n
Intensity of sound<\/td>\r\nI<\/span>=<\/span>(<\/span>\u0394<\/span>p<\/span>max<\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>2<\/span><\/span><\/span>2<\/span>\u03c1<\/span>v<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>I=(\u0394pmax)22\u03c1v<\/span><\/span><\/td>\r\n<\/tr>\r\n
Sound intensity level<\/td>\r\n\u03b2<\/span>(<\/span>d<\/span>B<\/span><\/span>)<\/span><\/span>=<\/span>10<\/span><\/span>log<\/span><\/span>10<\/span><\/span><\/span>(<\/span>I<\/span>I<\/span>0<\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03b2(dB)=10log10(II0)<\/span><\/span><\/td>\r\n<\/tr>\r\n
Resonant wavelengths of a tube closed at one end<\/td>\r\n\u03bb<\/span>n<\/span><\/span>=<\/span>4<\/span>n<\/span><\/span>L<\/span>,<\/span><\/span>n<\/span>=<\/span>1<\/span>,<\/span>3<\/span>,<\/span>5<\/span>,\u2026<\/span><\/span><\/span><\/span><\/span><\/span>\u03bbn=4nL,n=1,3,5,\u2026<\/span><\/span><\/td>\r\n<\/tr>\r\n
Resonant frequencies of a tube closed at one end<\/td>\r\nf<\/span>n<\/span><\/span>=<\/span>n<\/span>v<\/span>4<\/span>L<\/span><\/span><\/span>,<\/span><\/span>n<\/span>=<\/span>1<\/span>,<\/span>3<\/span>,<\/span>5<\/span>,\u2026<\/span><\/span><\/span><\/span><\/span><\/span>fn=nv4L,n=1,3,5,\u2026<\/span><\/span><\/td>\r\n<\/tr>\r\n
Resonant wavelengths of a tube open at both ends<\/td>\r\n\u03bb<\/span>n<\/span><\/span>=<\/span>2<\/span>n<\/span><\/span>L<\/span>,<\/span><\/span>n<\/span>=<\/span>1<\/span>,<\/span>2<\/span>,<\/span>3<\/span>,\u2026<\/span><\/span><\/span><\/span><\/span><\/span>\u03bbn=2nL,n=1,2,3,\u2026<\/span><\/span><\/td>\r\n<\/tr>\r\n
Resonant frequencies of a tube open at both ends<\/td>\r\nf<\/span>n<\/span><\/span>=<\/span>n<\/span>v<\/span>2<\/span>L<\/span><\/span><\/span>,<\/span><\/span>n<\/span>=<\/span>1<\/span>,<\/span>2<\/span>,<\/span>3<\/span>,\u2026<\/span><\/span><\/span><\/span><\/span><\/span>fn=nv2L,n=1,2,3,\u2026<\/span><\/span><\/td>\r\n<\/tr>\r\n
Beat frequency produced by two waves that\r\n
<\/div>\r\ndiffer in frequency<\/td>\r\n
f<\/span>beat<\/span><\/span><\/span>=<\/span>\u2223\u2223<\/span>f<\/span>2<\/span><\/span>\u2212<\/span>f<\/span>1<\/span><\/span><\/span>\u2223\u2223<\/span><\/span><\/span><\/span><\/span><\/span><\/span>fbeat=|f2\u2212f1|<\/span><\/span><\/td>\r\n<\/tr>\r\n
Observed frequency for a stationary observer\r\n
<\/div>\r\nand a moving source<\/td>\r\n
f<\/span>o<\/span><\/span>=<\/span>f<\/span>s<\/span><\/span>(<\/span>v<\/span>v<\/span>\u2213<\/span>v<\/span>s<\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>fo=fs(vv\u2213vs)<\/span><\/span><\/td>\r\n<\/tr>\r\n
Observed frequency for a moving observer\r\n
<\/div>\r\nand a stationary source<\/td>\r\n
f<\/span>o<\/span><\/span>=<\/span>f<\/span>s<\/span><\/span>(<\/span>v<\/span>\u00b1<\/span>v<\/span>o<\/span><\/span><\/span>v<\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>fo=fs(v\u00b1vov)<\/span><\/span><\/td>\r\n<\/tr>\r\n
Doppler shift for the observed frequency<\/td>\r\nf<\/span>o<\/span><\/span>=<\/span>f<\/span>s<\/span><\/span>(<\/span>v<\/span>\u00b1<\/span>v<\/span>o<\/span><\/span><\/span>v<\/span>\u2213<\/span>v<\/span>s<\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>fo=fs(v\u00b1vov\u2213vs)<\/span><\/span><\/td>\r\n<\/tr>\r\n
Mach number<\/td>\r\nM<\/span>=<\/span>v<\/span>s<\/span><\/span><\/span>v<\/span><\/span><\/span><\/span><\/span><\/span><\/span>M=vsv<\/span><\/span><\/td>\r\n<\/tr>\r\n
Sine of angle formed by shock wave<\/td>\r\nsin<\/span><\/span>\u03b8<\/span>=<\/span>v<\/span>v<\/span>s<\/span><\/span><\/span><\/span>=<\/span>1<\/span>M<\/span><\/span><\/span><\/span><\/span><\/span><\/span>sin\u03b8=vvs=1M<\/span><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/section><\/div>\r\n<\/div>\r\n
\r\n
\r\n

Summary<\/span><\/h3>\r\n
\r\n
\r\n

17.1<\/span>\u00a0<\/span>Sound Waves<\/span><\/h4>\r\n