Question

define the time period of wave

Answer 1

Time period of an wave :
The time needed for one complete cycle of vibration to pass a given point is called time period of an wave.
Time period decreases if frequency of the wave increases.

Hope it is useful to you.

Answer 2

Consider a wave having Amplitude (A), angular frequency $\bold{(\omega)}$

Making x = 0 and initial phase$\bold{(\phi)}$ = 0.

Diagram

$\setlength{\unitlength}{2cm}\begin{picture}(1,1)\linethickness{0.4mm}\put(-0.4,1){\bold{y(t)}}\put(0,1){\vector(0,-1){2}}\put(0,0){\vector(2,0){2.6}}\put(0,0){\vector(0,1){1.7}}\qbezier(0,0)(0.3,1.5)(0.8,0)\qbezier(0.8,0)(1.3,-1.5)(1.6,0)\qbezier(1.6,0)(1.9,1.5)(2.4,-0.3)\put(0,0.9){\vector(1,0){0.3}}\put(0,1.2){\vector(1,0){2}}\put(0.06,1.02){(t)} \put(1,1.3){(T+t)} \put(2.6,-0.2){Time}\end{picture}$

∴ the equation for displacement at time (t) becomes,

 $\bold{\tt y(t)=Asin(\omega t)}$......equ(1)

The same displacement is obtained at time (T+t).

∴ $\bold{\mathff{y(T+t)=Asin \omega (T+t)}}$

or, $\bold{\mathff{y(T+t)=Asin(\omega T+\omega t)}}$.....equ(2)

The displacement is same

⇒ Asin ($\bold{\omega}$t) = A sin($\bold{\omega}$T+$\bold{\omega}$t)

or, sin($\bold{\omega}$t) = sin($\bold{\omega}$T+$\bold{\omega}$t)

⇒ $\bold{\omega}$T = 2π

$\bold{\mathff{T=\dfrac{2 \pi}{\omega}}}$