Wave Characteristics
Wave Motion of Class 11
Wave Characteristics
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.
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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. |
(a)(b) 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.
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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. |
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Wave Dimension
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.
Wave PulseIf 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). |
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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.
Wave Train
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.
