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A STRING VIBRATES WITH FREQUENCY 200HZ ITS LENGTH INCREASED TO 4/3 TIMES THE INITIAL LENGHT AND TENSION IS ADJUSTED TILL THE STRING VIBRATES WITH FREQUENCY 300 HZ . WHAT IS THE RATIOOF THE NEW TENION TO THE ORIGINAL TENSION
The ratio is 4:1.
we know that V=root(T/u)
where V is the velocity of the string
T is the tension of the string
u is the linear density of the string
and V=fx#
where f is the freqency and # is the wavelength.
therefore f is proportional to root(T/u)
thus 200xroot(u/Ti)=300xroot((3/4u)/Tf)
therefore Tf/Ti=27/16
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