Name: Velocity and Acceleration of Particles in Wave Motion
Uploaded: 2019-07-19
Duration: 7 min 3 s
Description: We know that there is no net movement of particles in a wave, but they vibrate at their place. The video discusses the velocity and acceleration of the parti...

Question

What do you understand by wave function? Explain periodic wave functions and harmonic wave functions.

Accepted Answer

The functions which describe the motion of a wave pulse are called the Wave function.

Let's consider that a wave pulse is moving in a stretched string from left to right.

Let the free end $O$ of the string be the origin and $O A$ positive direction of $X$ -axis. When the free end is given a sudden jerk perpendicular to $O A$ , a wave pulse produced at $O$ start travelling along the string.

At $t = 0$ , the displacement $y$ of the wave pulse at a point $P$ , distant $x$ from $O$ , is represented by,

$y = f (x)$

Now, if wave pulse travels with speed $v$ without a change in shape, then displacement $(x + v t)$ from the origin at time $t$ would be the same as that of the point $x$ at $t = 0$ . So, the displacement function will be,

$y (x, t) = f (x - v t)$

Periodic Wave Function $:$ A periodic wave function represents a train of identical wave pulses which repeat after a fixed distance, or after a fixed interval of time.

In Periodic wave, the displacement repeats itself after a fixed interval of time $T$ . Then,

$y (x, t + T) = y (x, t) = f (x - v t)$

Harmonic Wave Function $:$ Harmonic waves are a periodic wave in which the particles o the medium undergo simple harmonic motion. Therefore, in a harmonic wave function, the function is a sine or cosine function.

A complete harmonic wave function is described as,

$y (x, t) = a \sin [\frac{2 π}{λ} (v t - x) + ϕ_{0}]$

Where, $ϕ_{0}$ is the initial phase angle of the wave.

What do you understand by wave function? Explain periodic wave functions and harmonic wave functions.

Important Questions on Progressive Harmonic Waves

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