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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

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


 

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2 Answers

Aditi Bhatnagar
31 Points
10 years ago

The ratio is 4:1.

G Narayana Raju
51 Points
10 years ago

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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