document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=80761>Question 80761</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please HELP HELP!!!  Please help explain and show what is the decibel level of a normal conversation,(square root of 10)- 3.2 x watt per meter^2?   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #57955 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=57955\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What is the decibel level of a normal conversation,(square root of 10)- 3.2 x watt per meter^2?<BR>\n" );
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document.write( "I'm not sure what your problem is supposed to be. The opening statement asks what is the <BR>\n" );
document.write( "decibel level of a normal conversation. After that you have written <BR>\n" );
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document.write( "(square root of 10)- 3.2 watts per meter^2?<BR>\n" );
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document.write( "That is not a decibel level because the decibel level has units of decibels, not watts/m^2.<BR>\n" );
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document.write( "The units of watts/m^2 sort of implies that you are to take the decibel level of normal<BR>\n" );
document.write( "conversation and find the sound energy in that level of normal conversation.<BR>\n" );
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document.write( "Normal conversation is about 65 decibels.<BR>\n" );
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document.write( "The equation that defines the decibel level of sound is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+10%2ALog%28P%5B2%5D%2FP%5B1%5D%29 ALIGN=MIDDLE  ALT=\"D+=+10%2ALog%28P%5B2%5D%2FP%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "in which D is the number of decibels; Log is Log operator to the base 10; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5B2%5D ALIGN=MIDDLE  ALT=\"P%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is<BR>\n" );
document.write( "the sound energy, in this problem it is the energy of the sound in normal conversation;<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5B1%5D ALIGN=MIDDLE  ALT=\"P%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the energy of sound that is the lowest sound energy that can be heard.<BR>\n" );
document.write( "The internationally accepted standard for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5B1%5D ALIGN=MIDDLE  ALT=\"P%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E%28-12%29 ALIGN=MIDDLE  ALT=\"10%5E%28-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > watts/m^2 ... the<BR>\n" );
document.write( "least amount of sound energy that is audible.<BR>\n" );
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document.write( "If you are to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5B2%5D ALIGN=MIDDLE  ALT=\"P%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the sound energy of normal conversation, you can do so if<BR>\n" );
document.write( "you say that the decibel level of normal conversation is 65 decibels. All you have to<BR>\n" );
document.write( "do is use the equation that defines decibels and substitute the values for D and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5B1%5D ALIGN=MIDDLE  ALT=\"P%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "As was noted, D = 65 and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5B1%5D+=+10%5E%28-12%29 ALIGN=MIDDLE  ALT=\"P%5B1%5D+=+10%5E%28-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substituting those two values into the<BR>\n" );
document.write( "equation results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=65+=+10%2ALog%28P%5B2%5D%2F%2810%5E%28-12%29%29%29 ALIGN=MIDDLE  ALT=\"65+=+10%2ALog%28P%5B2%5D%2F%2810%5E%28-12%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Recall that by the rules of Logarithms, if you take the Logarithm of a fractional <BR>\n" );
document.write( "term, an equivalent is the Logarithm of the numerator minus the Logarithm of the denominator.<BR>\n" );
document.write( "Applying this rule to the equation above results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=65+=+10%2A%28Log%28P%5B2%5D%29+-+Log%2810%5E%28-12%29%29%29 ALIGN=MIDDLE  ALT=\"65+=+10%2A%28Log%28P%5B2%5D%29+-+Log%2810%5E%28-12%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Also recall that by the rules of Logarithms, if you have the Logarithm of a quantity that<BR>\n" );
document.write( "has an exponent, an equivalent is the exponent times the Log of just the quantity.<BR>\n" );
document.write( "Apply this rule to the last term on the right side of the equation and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=65+=+10%2A%28Log%28P%5B2%5D%29-%28-12%29%2ALog%2810%29%29 ALIGN=MIDDLE  ALT=\"65+=+10%2A%28Log%28P%5B2%5D%29-%28-12%29%2ALog%2810%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "But, the Log to the base 10 of 10 is just 1. So, substitute 1 for Log(10) to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=65+=+10%2A%28Log%28P%5B2%5D%29+-+%28-12%29%2A1%29 ALIGN=MIDDLE  ALT=\"65+=+10%2A%28Log%28P%5B2%5D%29+-+%28-12%29%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Note that -(-12)*1 is just +12.  Substitute this and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=65+=+10%2A%28Log%28P%5B2%5D%29+%2B+12%29 ALIGN=MIDDLE  ALT=\"65+=+10%2A%28Log%28P%5B2%5D%29+%2B+12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiplying out the right side results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=65+=+10%2ALog%28P%5B2%5D%29+%2B+120 ALIGN=MIDDLE  ALT=\"65+=+10%2ALog%28P%5B2%5D%29+%2B+120\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Subtract 120 from both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-55+=+10%2ALog%28P%5B2%5D%29 ALIGN=MIDDLE  ALT=\"-55+=+10%2ALog%28P%5B2%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Divide both sides by 10 to find that:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5.5+=+Log%28P%5B2%5D%29 ALIGN=MIDDLE  ALT=\"-5.5+=+Log%28P%5B2%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Convert this to exponential form and you have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E%28-5.5%29+=+P%5B2%5D ALIGN=MIDDLE  ALT=\"10%5E%28-5.5%29+=+P%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Calculator time.  Raise 10 to the -5.5 power and the answer is in scientific notation is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.16227766+%2A+10%5E%28-6%29 ALIGN=MIDDLE  ALT=\"3.16227766+%2A+10%5E%28-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "That means that:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5B2%5D+=+3.16227766+%2A+10%5E%28-6%29 ALIGN=MIDDLE  ALT=\"P%5B2%5D+=+3.16227766+%2A+10%5E%28-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > watts/m^2<BR>\n" );
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document.write( "Hope that I guess correctly what this problem was asking you to do. If you have a value<BR>\n" );
document.write( "for the decibels for normal conversation and you need to find the sound energy of normal<BR>\n" );
document.write( "conversation, just use this method only substitute your db value in place of 65 and work<BR>\n" );
document.write( "it out.  You'll probably need to re-post this problem if I guessed wrong. If you do re-post,<BR>\n" );
document.write( "clarify what you are looking for, what that last term involving watts/m^2 is, and any<BR>\n" );
document.write( "other information you want considered.<BR>\n" );
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document.write( "Hope this helps you to understand the problem a little better too. <BR>\n" );
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document.write( "Cheers! </SPAN>\n" );
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