document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1100491>Question 1100491</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the frequency of vibration of a given string is directly proportion to the square root of the tension T and inversely proportional to the length L and the diameter D ,if T is increased by 50% and L is halved, calculate the percentage change in the frequency </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #714990 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=714990\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y = k * x is direct variation formula.<BR>\n" );
document.write( "y = k / x is inverse variation formula.<BR>\n" );
document.write( "z = k * x / y is direct and inverse variation formula combined.\r<BR>\n" );
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document.write( "k is the constant of proportionality.\r<BR>\n" );
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document.write( "the frequency of vibration of a string is directly proportional to the square root of the tension T and inversely proportional to the length L and the diameter D.\r<BR>\n" );
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document.write( "i believe that, when they say inversely proportional to the length L and the diameter D, that they mean inversely proportional to L * D.\r<BR>\n" );
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document.write( "assuming that interpretation is correct, your formula will become V = (K * T) / (L * D).\r<BR>\n" );
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document.write( "if  T is increased by 50% and L is halved, the formula would become:\r<BR>\n" );
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document.write( "V = (1.5 * K * T) / (.5 * L * D)\r<BR>\n" );
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document.write( "this can be simplified to V = (3 * K * T) / (L * D).\r<BR>\n" );
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document.write( "the frequency would be equal to 3 times what it was.\r<BR>\n" );
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document.write( "3 times what it was is 300% of what it was.\r<BR>\n" );
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document.write( "the frequency would be equal to 2 times more than what it was.\r<BR>\n" );
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document.write( "that would be an increase of 200% more than what it was.\r<BR>\n" );
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document.write( "i think, by change, they mean what it became, and, in my mind, it became 300% of what it was, so i would go with 300%.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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