Answer
The length of the cord is 21 meters.
Work Step by Step
We can write an expression for the speed $v$ of the vibrations. Let $L$ be the length of the cord.
$v = \frac{L}{t}$
We can write another expression for the speed of the vibrations.
$v = \frac{F_T}{\mu} = \sqrt{\frac{F_T}{m/L}}$
To find the length $L$, we can equate the two expressions for the speed $v$.
$\frac{L}{t} = \sqrt{\frac{F_T}{m/L}}$
$\frac{L^2}{t^2} = \frac{F_T~L}{m}$
$L = \frac{F_T~t^2}{m}$
$L = \frac{(35~N)(0.55~s)^2}{0.50~kg}$
$L = 21~m$
The length of the cord is 21 meters.