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| Wave Properties |
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| On observing waves, it may be observed that they travel with a definite speed through a uniform medium. If we watch a particular spot, we find that the waves pass that spot at regular intervals of time. The following definitions help in describing wave motion. |
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| The period of wave motion is the time in which a particle of the medium completes one oscillation i.e., a to and fro motion about its mean position. |
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It is the number of waves produced per second or the number of oscillations made by a particle of the medium per second. In T seconds one oscillation is completed. Therefore in 1 second the
number of oscillations made will be  This is the
definition of frequency.
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| It is the distance travelled by the wave in the time in which a particle of the medium completes one oscillation. In the case of a transverse wave, the distance between the centres of two nearest crests or between the centres two nearest troughs gives the wavelength. In the case of a longitudinal wave, the distance between the centres of two nearest compressions or between the centres of two nearest rarefactions gives the wavelength. |
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| The distance travelled by the wave in one second gives its velocity. In a time equal to the period, the wave covers a distance equal to
wavelength (l).
But according to equation 1.1, |
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| It is the maximum displacement of a particle of the medium from its mean position. |
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| When a wave passes through a medium, the particles of the medium vibrate about their respective mean positions in the same manner, but reach the corresponding positions in their paths at different instants of time. These relative positions represent the phase of the motion. It is measured either in terms of the angle that the particle has described (denoted as a fraction of 2p) or the time that has elapsed (measured as a fraction of the time period T), since the particle last passed through its mean position in the positive direction. |
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| The phase difference between any two particles indicates the extent by which they are out of step with each other. |
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| For example, a particle on the crest and a particle on the adjacent trough of a wave differ in phase by 180o or p radians. |
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| Wavefront |
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| A surface on which all the particles of the medium are in identical state of motion at a given instant, is called a wavefront. It is the locus of all the points which are in the same phase. In a homogenous and isotropic medium, the wave front is always perpendicular to the direction of propagation of the wave. |
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It is defined as the rate of change of
phase with time. One full wave (i.e., a crest and a trough) is associated with a phase change of 360o or 2p radians. The time required for this change is the period T. Thus, the angular frequency  |
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| It is defined as the space rate of change of phase. In a distance l, a phase change of 2p occurs. |
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| It must be noted that when a wave passes from one medium to another, its velocity changes. In this process the frequency remains the same, but the wavelength changes in proportion to the velocity. |
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