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/T_i)=300xroot((3/4u)/T_f)

therefore T_f/T_i=27/16