Answer
The maximum speed of vibration is $2.5\times 10^{-6}~m/s$
Work Step by Step
We can find the angular frequency $\omega$:
$\omega = 2\pi~f = (2\pi)(4000~Hz) = 8000\pi~rad/s$
We can find the maximum speed:
$v_m = A~\omega$
$v_m = (0.10\times 10^{-9}~m)~(8000\pi~rad/s)$
$v_m = 2.5\times 10^{-6}~m/s$
The maximum speed of vibration is $2.5\times 10^{-6}~m/s$.
