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The fundamental frequency of the sonometer wire increases by 9 Hz if its tension is increased by 69%, keeping the length constant.The frequency  of the wire is 

Answer:

Explanation:

We know that freequency of vibration of a strtched string is given by 

$v=\frac{1}{2l}\sqrt{\frac{T}{m}}$

 where, T= tension in string

m= mass /length

 and l= length of string 

New freequency,

  $v'=v+9=\frac{1}{2l}\sqrt{\frac{T+(69/100)T}{m}}$

 $\Rightarrow $  $\frac{v}{v'}=\sqrt{\frac{T}{\frac{169}{100}T}}\Rightarrow \frac{v}{v+9}=\sqrt{\frac{100}{169}}=\frac{10}{13}$

 $\Rightarrow 13 v=10v+90$

 v=30 Hz