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Superposition of waves
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Wave Motion

2) Points related to Wave Motion:

1) Amplitude: The maximum displacement of a vibrating particle of the medium from the mean position.

2) Time period (T): The time taken by the particle to complete one vibration.

3) Frequency: The number of vibration in one second by the particle n = 1/T.

Angular Frequency

4) Wavelength : The distance between two consecutive particles vibrating in the same phase.

Or

The distance between two consecutive crests or trough.

Or

The distance between two consecutive compressions or rarefaction.

Here v is the velocity of wave.

is the wave propagation vector which is written as:

, being the unit vector along the direction of wave propagation then,

Fig (3)

3) Equations for the progressive Simple Harmonic Waves:

1) The equation of a wave moving along the direction of positive X-axis is

Where ‘a’ is the amplitude, is the phase difference and ‘y’ is the displacement of a particle.

2) The equation of a progressive wave moving along the direction of negative X-axis is

3) The general equation of wave moving along X-axis is:

4) Other equation for a progressive wave moving along the direction of positive X-axis is:

Is propagation constant or wave vector

Points to remember: Wave equation can be shown by any of the following relations:

All these waves are also called as ‘sinusoidal’ waves.

4) Necessary Condition for two particles to be in same phase or in opposite phase:

5) Intensity of waves, Energy Density:

1) Intensity (I): Amount of energy flowing per second from unit area of the medium in a direction perpendicular to the propagation of wave.

2) For a given medium ( and v are constants)

3) Unit of Intensity: Joule/m2 second or watt/m2.

4) Energy density (E): Energy per unit volume of the medium

5) For second waves the intensity obeys the inverse square law. If the distance between the source and the point of observation is ‘x’ then

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