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Learning Objectives (See related pages) Concepts and Skills to Review
gauge pressure (Section 9.5)
bulk modulus (Section 10.4)
relation between energy and amplitude in SHM (Section 10.5)
period and frequency in SHM (Section 10.6)
longitudinal waves, intensity, standing waves, superposition principle (Chapter 11)
logarithms (Appendix A.3) Mastering the Concepts
A sound wave can be described either by the gauge pressure p , which measures the pressure fluctuations above and below the ambient atmospheric pressure, or by the displacement s of each point in the medium from its undisturbed position.
Humans with excellent hearing can hear frequencies from 20 Hz to 20 kHz. The terms infrasound and ultrasound are used to describe sound waves with frequencies below 20 Hz and above 20 kHz, respectively.
The speed of sound in a fluid is <![CDATA[<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663820/ch12_1.JPG','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a>]]>
The speed of sound in an ideal gas at any absolute temperature T can be found if it is known at one temperature: <![CDATA[<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663820/ch12_2.JPG','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a>]]> T 0 is v0 .
The speed of sound in air at 0°C (or 273 K) is 331 m/s.
For sound waves traveling along the length of a thin solid rod, the speed is approximately <![CDATA[<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663820/ch12_3.JPG','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (2.0K)</a>]]>
The pressure amplitude of a sound wave is proportional to the displacement amplitude. For a harmonic sound wave at angular frequency w , <![CDATA[<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663820/ch12_4.JPG','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a>]]> u is the speed of sound and r is the mass density of the medium.
The intensity of a sound wave is related to the pressure amplitude as follows: <![CDATA[<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663820/ch12_5.JPG','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a>]]> r is the mass density of the medium and u is the speed of sound in that medium. The most important thing to remember is that intensity is proportional to amplitude squared , which is true for all waves, not just sound.
Sound intensity level in decibels is <![CDATA[<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663820/ch12_6.JPG','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a>]]> I0 = 10-12 W/m2 . Sound intensity level is useful since it roughly corresponds to the way we perceive loudness. Equal increments in intensity level roughly correspond to equal increases in loudness.
In a standing sound wave in a thin pipe, an open end is a pressure node and a displacement antinode; a closed end is a pressure antinode and a displacement node. <![CDATA[<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663820/ch12_7.JPG','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (3.0K)</a>]]> <![CDATA[<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663820/ch12_10.JPG','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (3.0K)</a>]]>
When two sound waves are close in frequency, the superposition of the two produces a pulsation called beats . <![CDATA[<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663820/ch12_8.JPG','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a>]]>
Doppler effect: if u s and u o are the velocities of the source and observer, the observed frequency is <![CDATA[<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663820/ch12_9.JPG','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (2.0K)</a>]]> u s and u o are positive in the direction of propagation of the wave and the wave medium is at rest.
