Answered

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The length of a violin string varies inversely as the frequency of its variations. A violin string 10 inches long vibrates at a frequency of 512 cycles per second. Find the frequency of an 8 inch violin string.

Sagot :

Pingwin09idn
Expressing it mathematically becomes
[tex]L \propto \frac{1}{f} [/tex]
As it varies, we change into equal sign and proportionality constant [tex]k[/tex]:
[tex]L= k(\frac{1}{f}) [/tex]
Since [tex]L = 10 in[/tex] and [tex]f = 512 cycles[/tex] are the first conditions, the second one has [tex]L = 8 in[/tex] with the unknown frequency. Because k is constant, equate the two conditions into one expression as
[tex]L_1f_1=L_2f_2[/tex]
For [tex]f_2[/tex],
[tex]f_2= \frac{L_1f_1}{L_2}= \frac{(10in)(512cycles)}{8in}=640cycles [/tex]









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