Wave Motion of Class 11
There are three wave characteristics used to classify mechanical waves:
1. the direction in which individual particles move when a wave passes by,
2. the dimensionality of the wave propagation
3. the particle behavior of the wave in time
Particle Motion with Respect to Wave Direction
If we watch a leaf on a pond as a ripple goes by we observe that it does not travel with the wave; it merely moves up and down at the same position. This fact implies that a wave transports both energy and momentum without transporting matter.
If the particles of the medium in which the wave is travelling move perpendicular to the direction of wave propagation, the wave is called transverse.
Fig.(14.1 a) shows how a small segment of a string moves as a transverse pulse passes. As the leading edge of the pulse reaches it, the segment moves perpendicular to the string’s equilibrium position. Its displacement reaches a maximum as the peak of the pulse passes and then returns to its equilibrium position after the pulse has moved on.
Fig.(14.1)(a) As a transverse pulse passes, a given element of a string undergoes only transverse displacements. The medium (the rope) is not carried along with the wave.
(b) On the leading edge of a pulse the particles are moving upward, whereas on the trailing edge the particles are moving downward.
It is obvious from the Fig.(14.1 b), that the particles on the leading edge are moving upward while those on the trailing edge are moving downward.
If the particles of the medium move parallel to the direction of wave propagation, the wave is said to be longitudinal. Fig. (14.2) shows a long and very elastic spring. When we repeatedly push and pull on ends of the spring, the compressions and stretches of the spring travel along the spring direction. A particle marked by dot on the spring moves back and forth, parallel and anti-parallel to the direction of the wave velocity.
One – Dimensional Waves
Wave confined to travel either to the right or left along a straight line are one-dimensional waves, e.g. wave produced on a string.
Two – Dimensional Waves
Waves that propagate over a surface are two-dimensional waves, e.g. vibration of the surface of a drum head.
Three – Dimensional Waves
Three – dimensional waves propagate in all directions, e.g. a sound wave.
Particle Behaviour in Time
The above two characteristics were related to spatial description of a wave. The third characteristic describes a wave behaviour in time.
If the motion of a particle within a restoring medium follows a time sequence that consists of equilibrium (no motion) followed in time by some type of motion, and finally a return to equilibrium, the wave is said to consist of a pulse.
We can generate a transverse wave pulse on a string by rapidly displacing one end of the string up and down, but just once as shown in Fig.(14.3 a).
As the displacement pulse travels along the string each particle in the string begins at rest, experiences a displacement as the pulse passes through it, and then returns to the equilibrium.
In a wave train the wave travels through the medium, and the medium’s particles undergo periodic motions. If the periodic motions are simple harmonic oscillations, the disturbance is called a sinusoidal wave train.
One can generate a wave train on a stretched string by continuously moving the end of the string up and down in simple harmonic motion as shown in Fig.(14.3 b). A wave train need not be sinusoidal; any continuous succession of pulses constitutes a wave train.