document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191776>Question 1191776</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The intensity level of sound is measured on a logarithmic scale. The intensity level, β, of sound is defined in the following equation β=10 log I/Io where β is measured in decibels, and Io is the intensity of a reference level. The reference level is 1.0x10^-12 w/m^2\r<BR>\n" );
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document.write( "How much louder does a siren at 30 m away, with an intensity of 1.0x10^-2 w/m^2, sound compared to a whisper, which is 20 decibels? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #823642 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=823642\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula is B = 10 * log(I/Io)<BR>\n" );
document.write( "B is the decibel level of the sound.<BR>\n" );
document.write( "I is the intensity level of the sound.<BR>\n" );
document.write( "Io is the intensity level of the reference.\r<BR>\n" );
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document.write( "the intensity level of the reference becomes:<BR>\n" );
document.write( "Io = 1 * 10^-12 * w/m^2<BR>\n" );
document.write( "w/m^2 equals watts per square meter.\r<BR>\n" );
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document.write( "when m = 30, the intensity level of the reference becomes:<BR>\n" );
document.write( "Io = 1 * 10^-12 * w/900.\r<BR>\n" );
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document.write( "if the intensity level of the siren is equal to 1 * 10^-2 * w/m^2.<BR>\n" );
document.write( "when m = 30, the intensity level of the siren is equal to 1 * 10^-2 * w/900.<BR>\n" );
document.write( "I = 1 * 10^-2 * w/900.\r<BR>\n" );
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document.write( "the decibel level of the siren becomes:<BR>\n" );
document.write( "B = 10 * log(1 * 10^-2 * w/900) / (1 * 10^-12 * w/900)<BR>\n" );
document.write( "the 1 and the w/900 cancel out and the equation becomes:<BR>\n" );
document.write( "B = 10 * log(10^-2/10^-12.<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "B = 10 * log(10^10) = 100 db\r<BR>\n" );
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document.write( "the decibel level has increased by 100, since the decibel level of the reference signal is 0.\r<BR>\n" );
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document.write( "the intensity level of the signal has increased by a factor of 10^10.<BR>\n" );
document.write( "this means that the intensity level of the siren is 10^10 times more than the intensity level of the reference level.<BR>\n" );
document.write( "10^10 is equal to 10 billion, i believe.<BR>\n" );
document.write( "the intensity level of the siren is 10 billion times the intensity level of the reference level.\r<BR>\n" );
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document.write( "you are given that the decibel level of a whisper is 20 db.<BR>\n" );
document.write( "this is presumed to also be at a distance of 30 meters from the source of the whisper.\r<BR>\n" );
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document.write( "since the siren is 100 db and the whisper is 20 db, then the siren is 80 db higher than the whisper.\r<BR>\n" );
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document.write( "80 db = 10 * log(I/Io)<BR>\n" );
document.write( "divide both sides of this equation by 10 to get:<BR>\n" );
document.write( "8 = log(I/Io)<BR>\n" );
document.write( "this is true if and only if I/Io = 10^8<BR>\n" );
document.write( "10^8 is equal to 100 million.\r<BR>\n" );
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document.write( "this says that the sound of the siren has an intensity level that is 100 million times the intensity level of a whisper, given they are both the same distance from the listener.<BR>\n" );
document.write( "that's what i think your solution is.\r<BR>\n" );
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document.write( "i think the rule of thumb is:<BR>\n" );
document.write( "for each 10 db increase, the intensity level is increased by a factor of 10.<BR>\n" );
document.write( "this means:<BR>\n" );
document.write( "10 db increase = 10 * the intensity level.<BR>\n" );
document.write( "20 db increase = 10^2 * the intensity level.<BR>\n" );
document.write( "30 db increase = 10^3 * the intensity level.<BR>\n" );
document.write( "....<BR>\n" );
document.write( "80 db increase = 10^8 * the intensity level.<BR>\n" );
document.write( "etc.\r<BR>\n" );
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document.write( "let me know if you have any questions.<BR>\n" );
document.write( "i'll try to answer as best i can.<BR>\n" );
document.write( "this is new to me, so take that into consideration.<BR>\n" );
document.write( "theo\r<BR>\n" );
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document.write( " </SPAN>\n" );
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