$20$ waves pass through a point in $2$ seconds. If the distance between one crest and adjacent trough is $1.5 \, m$,calculate: $(a)$ the frequency,$(b)$ the wavelength.

(N/A) The frequency $(v)$ is defined as the number of waves passing through a point per unit time.
Given that $20$ waves pass in $2$ seconds,the frequency is calculated as:
$v = \frac{20 \text{ waves}}{2 \text{ seconds}} = 10 \text{ Hz}$.
$(b)$ The distance between a crest and the adjacent trough is equal to half of the wavelength $(\frac{\lambda}{2})$.
Given that the distance is $1.5 \, m$,we have:
$\frac{\lambda}{2} = 1.5 \, m$.
Therefore,the wavelength $\lambda = 1.5 \times 2 = 3 \, m$.