Question

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

• A. $42Hz$
• B. $24Hz$
• C. $30Hz$
• D. $36Hz$

Answer 1

Answer: (C)

We know that, frequency of vibration of a stretched 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 frequency,
$v^{\prime }=v+9=\frac{1}{2l}\sqrt{\frac{T+(69/100)}{m}}$
$\Rightarrow \frac{v}{v^{\prime }}=\sqrt{\frac{T}{169}T}$
$\Rightarrow \frac{v}{v+9}=\sqrt{\frac{100}{169}}=\frac{10}{13}$
$\Rightarrow 13v=10v+90$
$v=30Hz$