State the relationship between frequency and time period of a wave. The wavelength of vibrations produced on the surface of water is $2 \, cm$. If the wave velocity is $16 \, m s^{-1}$, find its frequency and time period.

(N/A) The relationship between frequency $(v)$ and time period $(T)$ is given by $v = 1 / T$.
Given:
Wavelength $(\lambda)$ = $2 \, cm = 2 \times 10^{-2} \, m$
Wave velocity $(V)$ = $16 \, m s^{-1}$
To find frequency $(v)$:
Using the formula $V = v \lambda$, we get $v = V / \lambda$.
$v = 16 / (2 \times 10^{-2}) = 8 \times 10^2 = 800 \, Hz$.
To find time period $(T)$:
Using the formula $T = 1 / v$.
$T = 1 / 800 = 0.00125 \, s$ or $1.25 \times 10^{-3} \, s$.