Thank you for reporting, we will resolve it shortly
Q.
The length of the string of a musical instrument is $90\, cm$ and has a fundamental frequency of $120\, Hz$. Where should it be pressed to produce fundamental frequency of $180\, Hz$ ?
The velocity of the travelling wave remains a constant.
Initially for fundamental mode,
the length of the string is half the wavelength.
$
\begin{array}{l}
\lambda=180 cm \\
v=124 Hz
\end{array}
$
The new frequency is Given by: $v_{2}=186 Hz$
Using the fact that $v \lambda=$ constant
we get $\lambda_{2}=120 cm$
The midpoint of this would be the node (where the string needs to be plucked).
The string needs to be plucked at $60 cm$.