document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73487>Question 73487</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0132191415/algebrahomeworkh>college algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The loudness of sound is based on intensity level measured in decibels using a logarithmic scale and is relative to (a ratio of) the weakest sound the ear can hear.\r<BR>\n" );
document.write( "\n" );
document.write( "I am needing:<BR>\n" );
document.write( "The formula for measuring sound. <BR>\n" );
document.write( "Pick a specific sound, give the decibels of the sound, and explain what this measurement means. <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52860 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=52860\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are various measurements for sound ... pitch, frequency, amplitude, speed, loudness, phase,<BR>\n" );
document.write( "intensity, and wavelength are some of the measurements that can be made.  The one I think <BR>\n" );
document.write( "you are most interested in is the measure of sound pressures that are measured by a quantity <BR>\n" );
document.write( "called sound level.  Sound level is measured in decibels (dB).<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Sound level is a ratio of the pressure of a given sound wave to the pressure of the most <BR>\n" );
document.write( "faintly heard sound. The most faintly heard sound has a pressure of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A10%5E-5 ALIGN=MIDDLE  ALT=\"2%2A10%5E-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Newtons<BR>\n" );
document.write( "per square meter. (In scientific work Newtons per square meter is sort of the same thing as tire<BR>\n" );
document.write( "pressure in a bike or car tire.  Tire pressure, in the US at least, is normally measured in pounds per square inch.)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Anyhow, a sound level of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A10%5E-5 ALIGN=MIDDLE  ALT=\"2%2A10%5E-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Newtons per square meter is called 0 dB. All other<BR>\n" );
document.write( "sound levels are measured relative to that level.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The equation for the sound level S in decibels is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=10%2Alog%28P%2F%282%2A10%5E-5%29%29 ALIGN=MIDDLE  ALT=\"S=10%2Alog%28P%2F%282%2A10%5E-5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "where P is the measured pressure in Newtons per square meter and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A10%5E-5 ALIGN=MIDDLE  ALT=\"2%2A10%5E-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the <BR>\n" );
document.write( "reference level where sound is the lowest that can be heard. And log is the logarithm<BR>\n" );
document.write( "to the base 10.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "If an actual sound is 10 times the intensity of the reference the sound level will be increased<BR>\n" );
document.write( "by 10 dB. An actual sound intensity that is 100 times the reference level will compute to <BR>\n" );
document.write( "be 20 dB. That means that a sound intensity of 100 dB is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E12 ALIGN=MIDDLE  ALT=\"10%5E12\"   DISABLED_style= \"max-width:90%; height:auto;\" > times as great in <BR>\n" );
document.write( "intensity than the reference level. This is obviously not a linear relationship but to the<BR>\n" );
document.write( "human ear loudness is about right.  A 100 dB sound is as much louder than a 70 dB sound as <BR>\n" );
document.write( "the 70 dB sound is to a 40 dB sound.  <BR>\n" );
document.write( ".<BR>\n" );
document.write( "Your ear is not an exact instrument.  Its sensitivity depends on the frequency (pitch) and the <BR>\n" );
document.write( "sound level.  And the ear tends to provide different judgments of sound depending on<BR>\n" );
document.write( "whether the sound is a single tone or a mixture of various tones.  People generally feel that <BR>\n" );
document.write( "a 10 dB increase in sound level is about twice as loud as it was before the dB was cranked up.<BR>\n" );
document.write( "And sound intensity has to go up by about 3dB before most people can sense a change.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "As for typical sound levels: <BR>\n" );
document.write( ".<BR>\n" );
document.write( "Threshold of hearing is by definition 0 dB<BR>\n" );
document.write( "Normal breathing - about 10 dB<BR>\n" );
document.write( "A whisper is about 20 dB. <BR>\n" );
document.write( "A quiet library or home study room is about 40 dB. <BR>\n" );
document.write( "A classroom is about 50 dB. <BR>\n" );
document.write( "Normal speech is about 60 db. <BR>\n" );
document.write( "Busy street traffic is around 70 dB<BR>\n" );
document.write( "A diesel semi-truck motoring on down the highway is about 90 dB<BR>\n" );
document.write( "Loud rock music about 115 dB <BR>\n" );
document.write( "The threshold of pain around 120 dB<BR>\n" );
document.write( "Next to a jet engine about 140 dB.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Probably more than you wanted to know about sound, but maybe some of this will help. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );