Define the following terms and state their $SI$ units:
$(a)$ Wavelength $(b)$ Time period $(c)$ Amplitude.
Establish the relation $V = v \lambda$,where the symbols have their usual meanings.

(N/A) Wavelength: It is defined as the distance travelled by a wave during the time a particle of the medium completes one vibration. It is denoted by $\lambda$. Its $SI$ unit is metre $(m)$.
$(b)$ Time period: It is defined as the time taken by a vibrating particle to complete one vibration. It is denoted by $T$. Its $SI$ unit is second $(s)$.
$(c)$ Amplitude: It is defined as the maximum displacement produced in the vibrating particle on either side of the mean position. It is denoted by $A$. Its $SI$ unit is metre $(m)$.
Derivation of the relation $V = v \lambda$:
We know that,wavelength $\lambda$ is the distance covered by the wave during the time a particle of the medium completes one vibration,i.e.,$T$.
Velocity of the wave $(V)$ is defined as:
$V = \frac{\text{Distance travelled by the wave}}{\text{Time taken}} = \frac{\lambda}{T}$
Since frequency $v = \frac{1}{T}$,substituting this into the equation:
$V = v \lambda$