document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=414299>Question 414299</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The frequency or number (f) of vibration of a string  under constant tension is inversely proportional to the length (l) of the string. If a string of 48 cm   <BR>\n" );
document.write( "vibrates 192 cycles per second, find the the constant of proportionality and the number of vibrations per second a string of 32 cm will make. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #290613 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=290613\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> direct and inverse proportion formulas are shown below:\r<BR>\n" );
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document.write( "y = k*x (direct proportion)\r<BR>\n" );
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document.write( "y = k/x (inverse proportion)\r<BR>\n" );
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document.write( "Since you are dealing with inverse proportion, then the second formula applies.\r<BR>\n" );
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document.write( "k is the constant of proportionality.\r<BR>\n" );
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document.write( "you are given that a string of 48 cm vibrates 192 cycles per second.\r<BR>\n" );
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document.write( "you can use this fact to find the constant of proportionality.\r<BR>\n" );
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document.write( "let y = number of cycles per second.<BR>\n" );
document.write( "let x = length of the string.\r<BR>\n" );
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document.write( "y = k/x becomes 192 = k/48\r<BR>\n" );
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document.write( "multiply both sides of this equation by 48 to get:\r<BR>\n" );
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document.write( "k = 192 * 48 = 9216\r<BR>\n" );
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document.write( "that's your constant of proportionality.\r<BR>\n" );
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document.write( "you apply that constant of proportionality when x = 32 cm.\r<BR>\n" );
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document.write( "you get y = 9216 / 32 = 288\r<BR>\n" );
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document.write( "the string will vibrate 288 cycles per second when the length of the string is 32 cm.\r<BR>\n" );
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document.write( "you can see that the proportion is inverse because, as the string length increases, the number of vibrations per second decreases.\r<BR>\n" );
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document.write( "you can also see that the ratio of the short string to the long string is inversely proportional as shown in the following table.\r<BR>\n" );
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document.write( "long string          short string        ratio of short string to long string\r\n" );
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document.write( "l = 48               l = 32              32/48 = 2/3\r\n" );
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document.write( "vbs = 192            vbs = 288           288/192 = 3/2\r\n" );
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document.write( "</PRE>\r<BR>\n" );
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document.write( "l = length<BR>\n" );
document.write( "vbs = vibrations per second\r<BR>\n" );
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document.write( " </SPAN>\n" );
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