Lesson_5.3b_Printable

Lesson_5.3b_Printable - Harmonic Stationary Waves Let us...

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Harmonic Stationary Waves Let us look at the direction of displacements of the particles as a wave advances in a medium. A particle on the crest of a wave has reached the maximum upward displacement and is now ready to move down A particle in a trough has reached the maximum downward displacement and is now ready to move up. What will be the state of vibration of a particle that is on the crest of one wave and in the trough of a second wave?. That particle will have no displacement The result of such a superposition is destruction. 1
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If the particle is on the crest of both waves, the displacements add up and the superposition is constructive . Two waves meeting at a point can interfere constructively or destructively producing a bigger wave or sometimes no wave. 2
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A mechanical driver attached to one end of a stretched string sets that end into up and down vibrations sending wave pulses down the length of the string. These wave pulses get reflected at the pulley Each particle on the string is subjected to displacements due to advancing and reflected waves. 3
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The instant when the crest and trough of both waves coincide, the string segments have maximum displacements. Advancing wave reflected wave This happens only for an instant as the waves are advancing in the opposite directions. 4
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Soon the crest of the advancing wave falls on the trough of the reflected wave. Since all the segments now are subjected to opposite displacements, they all remain stationary. 5
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This process repeats in time producing the states of maximum and minimum displacement alternatively. N N N A A Some points on the string will be permanently at rest and they are called nodal points ( N ) Points where the string segments have maximum displacements are called antinodes ( A ) The process of maximum and minimum displacements appearing and disappearing is called the formation of stationary waves . 6
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N N N A A he wavelength f the stationary wave is λ The wavelength λ of the stationary wave is the distance between two alternate nodes. Wavelength is the length of two full loops.
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This note was uploaded on 05/01/2011 for the course PHY 2048 taught by Professor George during the Fall '10 term at Edison State College.

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Lesson_5.3b_Printable - Harmonic Stationary Waves Let us...

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