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<HTML> <HEAD> <TITLE>Inverse Square Law for Sound</TITLE> </HEAD> <body bgcolor="#FFE4C8">  <A Name="c1"></A> <TABLE WIDTH="670" HEIGHT="370" BORDER="1" CELLSPACING="2" CELLPADDING= "2"> <TR> <TD WIDTH="604" HEIGHT="309"> <H1 align=center>Inverse Square Law, Sound</H1> <p>The <a href="../sound/intens.html#c1">sound intensity</a> from a point source of sound will obey the <a href= "../forces/isq.html#isq" >inverse square law</a> if there are no reflections or <a href= "reverb.html#c1" >reverberation</a>. A <a href="#c2">plot</a> of this intensity drop shows that it drops off rapidly. </p> <center><img src="imgaco/isqb.gif"></center> <center><table BORDER="1" CELLSPACING="2" CELLPADDING= "2"><tr><td><a href="#c2"><font size="+2"><a href="#c3">Calculation</a></font></a></td><td><a href="#c4"><font size="+2"><a href="isprob.html#c3">Intensity ratios</a></font></a></td><td><a href="#c4"><font size="+2"><a href="roomi.html#c1">Measurement example</a></font></a></td></tr></table></center> <center><table BORDER="1" CELLSPACING="2" CELLPADDING= "2"><tr><td rowspan="2">Other examples of inverse square law behavior:</td><td><a href="../forces/isq.html#isqg">Gravity</a></td><td><a href="../forces/isq.html#isqe">Electric</a></td></tr><tr><td><a href="../forces/isq.html#c4">Radiation</a></td><td><a href="../vision/isql.html#c1">Light</a></td></tr></table></center> </TD> <TD WIDTH="66" align=center><a href="../hframe.html">Index</a><BR><BR><a href="../sound/dbcon.html#c1">Sound level measurement</a><BR><BR><a href="auditcon.html#c1">Auditorium acoustics</a></TD></TR> <TR> <TD HEIGHT="17"> <table><tr><td width= "450"><A HREF="../hph.html"> HyperPhysics</A>*****<A HREF="../sound/soucon.html"> Sound </A></td><td align=right><font size="-1"><i>R Nave</i></font></td></tr></table></TD> <TD><a href="Javascript:history.go(-1)">Go Back</a></TD></TR> </TABLE> <BR><BR><BR><BR><BR><BR><BR><BR> <A Name="c2"></A> <TABLE WIDTH="580" HEIGHT="370" BORDER="1" CELLSPACING="2" CELLPADDING= "2"> <TR> <TD WIDTH="514" HEIGHT="309"> <H1 align=center>Inverse Square Law Plot</H1> <p>A plot of the drop of <a href="../sound/intens.html#c1">sound intensity</a> according to the <a href="#c1">inverse square law</a> emphasizes the rapid loss associated with the inverse square law. In an <a href="isprob.html#c2">auditorium</a>, such a rapid loss is unacceptable. It is mitigated by the <a href= "reverb.html#c1" >reverberation</a> in a good auditorium. This plot shows the points connected by straight lines but the actual drop is a smooth curve between the points. <center><img src="imgaco/isplot.gif"></center> </TD> <TD WIDTH="66" align=center><a href="../hframe.html">Index</a><BR><BR><a href="dbcon.html#c1">Sound level measurement</a><BR><BR><a href="auditcon.html#c1">Auditorium acoustics</a></TD></TR> <TR> <TD HEIGHT="17"> <table><tr><td width= "450"><A HREF="../hph.html"> HyperPhysics</A>*****<A HREF="../sound/soucon.html"> Sound </A></td><td align=right><font size="-1"><i>R Nave</i></font></td></tr></table></TD> <TD><a href="Javascript:history.go(-1)">Go Back</a></TD></TR> </TABLE> <BR><BR><BR><BR><BR><BR><BR><BR> <A Name="c3"></A> <TABLE WIDTH="670" HEIGHT="370" BORDER="1" CELLSPACING="2" CELLPADDING= "2"> <TR> <TD WIDTH="604" HEIGHT="309"> <H1 align=center>Sound Intensity from a Point Source</H1> <p> Sound from a point source obeys the <a href="#c1">inverse square law</a>. It's <a href="../sound/intens.html#c1">intensity</a> in <a href="../sound/db.html#c1">decibels</a> can be calculated by comparing the intensity to the <a href="../sound/intens.html#c3">threshold of hearing</a>. </p> <SCRIPT LANGUAGE ="JavaScript"> function sq(x){return x*x} function ical(){fh=document.forms[0];def();i0=Math.pow(10,-12);ii=fh.p.value/(4*Math.PI*sq(fh.r.value));fh.ib.value=snb(ii);fh.ip.value=snp(ii);dbb=10*Math.log(ii/i0)/Math.LN10;fh.i.value=dbb} function ur(rr){fh=document.forms[0];fh.r.value=rr;fh.rc.value=rr/.3048;ical()} function ui(db){fh=document.forms[0];ii=Math.pow(10,db/10)*Math.pow(10,-12);fh.ib.value=snb(ii);fh.ip.value=snp(ii);fh.p.value=ii*4*Math.PI*sq(fh.r.value)} function ui2(){fh=document.forms[0];ii=fh.ib.value*Math.pow(10,fh.ip.value);i0=Math.pow(10,-12);dbb=10*Math.log(ii/i0)/Math.LN10;fh.i.value=dbb;fh.p.value=ii*4*Math.PI*sq(fh.r.value)}   function sn(b,p){return b*Math.pow(10,p)}  function snp(x){return Math.round(Math.log(x)/Math.LN10)}  function snb(x){return x/Math.pow(10,snp(x))}  function svb(b,p){n=sn(b,p);return snb(n)}  function svp(b,p){n=sn(b,p);return snp(n)}   function def(){fh=document.forms[0];if (fh.p.value==0)fh.p.value=1;if (fh.r.value==0)fh.r.value=1} </script> <FORM method="" action=""> <p>At a distance r = <INPUT Type="text" Name="r" Value="" Size="6"onChange=ur(this.value)>m = <INPUT Type="text" Name="rc" Value="" Size="6"onChange=ur(this.value*.3048)>ft</p> <p>from a point source of acoustic power P = <INPUT Type="text" Name="p" Value="" Size="6"onChange=ical()> watts </p> <p>the sound intensity is <INPUT Type="text" Name="ib" Value="" Size="6"onChange=ui2()> x10^ <INPUT Type="text" Name="ip" Value="" Size="6"onChange=ui2()> watts/m<sup>2</sup> = <INPUT Type="text" Name="i" Value="" Size="6"onChange=ui(this.value)> dB.</p> <center><img src="imgaco/isc2.gif" usemap="#lcon"></center> <map name="lcon"> <area shape=rect coords="480,145,590,180" href= "invsqc.html#c1" > </map> </form> <center><table BORDER="1" CELLSPACING="2" CELLPADDING= "2"><tr><td><a href="../sound/db.html#c1">Decibel definition</a></td><td><a href="../sound/db.html#c3">Decibel calculation</a></td></tr></table></center> <center><table BORDER="1" CELLSPACING="2" CELLPADDING= "2"><tr><td><a href="isprob.html#c3">Calculating dB for distance ratios</a></td></tr></table></center> <center><table BORDER="1" CELLSPACING="2" CELLPADDING= "2"><tr><td><a href="isprob2.html#c1">Estimating sound levels in decibels </a></td></tr></table></center> </TD> <TD WIDTH="66" align=center><a href="../hframe.html">Index</a><BR><BR><a href="../sound/dbcon.html#c1">Sound level measurement</a><BR><BR><a href="auditcon.html#c1">Auditorium acoustics</a></TD></TR> <TR> <TD HEIGHT="17"> <table><tr><td width= "450"><A HREF="../hph.html"> HyperPhysics</A>*****<A HREF="../sound/soucon.html"> Sound </A></td><td align=right><font size="-1"><i>R Nave</i></font></td></tr></table></TD> <TD><a href="Javascript:history.go(-1)">Go Back</a></TD></TR> </TABLE> <BR><BR><BR><BR><BR><BR><BR><BR> <BR><BR><BR><BR><BR><BR> <BR><BR><BR><BR> </BODY> </HTML>