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| Transverse and Longitudinal Waves |
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| In this type of wave motion, the particles of the medium vibrate at right angles to the direction of propagation of the wave. |
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| Here are a few examples of transverse wave motion. |
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 waves formed on the surface of water |
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 waves along a stretched string |
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 electromagnetic waves |
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| The formation of a transverse wave can be illustrated with the following example. |
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Let P1, P2, P3, P4 ……………. ,etc., denote
neighboring particles of a medium which is in an undisturbed condition. Let the particle P1 be disturbed and made to move up and down with a period T. Let the
disturbance reach from one particle to the next particle in a time . |
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Thus, after a time
the disturbance reaches P2, which therefore begins to vibrate.
After a time  , P3 picks up the vibration.
In
this way, after a time T, the disturbance will have just reached P9. At this stage, P1 and P9 will be in the same state of vibration or will be in phase. The trough (valley) and the crest (hump) together, constitute one wave. The distance between P1 and P9 gives the wave length.
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The wave motion apparatus can be used to demonstrate the formation of the transverse waves. It consists of a number of metal rods of identical length passed through equidistant holes on a horizontal wooden plank. The upper end of each rod carries a small ball while the lower end rests on the groove over the rim of a circular metal disc. The discs are all rigidly attached to a common horizontal shaft with their planes vertical and parallel to each other. The shaft does not pass through the
center of any disc but through a different point. The eccentricity of the discs is so adjusted that there is a certain gradual angular displacement with respect to each other. When the shaft is rotated, each rod moves up and down. The balls attached to the rods, execute simple harmonic motion with a gradually changing phase difference between the successive balls. A transverse wave appears to progress in the horizontal direction with the formation of crests and troughs.
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| The above figure shows the formation of a transverse wave pulse in a rope. One end of a long rope is attached to a rigid support and the free end is given a sudden jerk, causing an up and down motion. The hump produced near the hand begins to move away from the hand. If the hand is repeatedly moved up and down, then instead of a pulse, a succession of pulses will follow one another as shown in the above figure. |
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| The particles of the rope move up and down, while the wave travels horizontally along the rope. Thus, the wave motion is transverse. |
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| This type of wave motion is possible in media which possess elasticity of shape or rigidity i.e., in solids. However, they are also observed on the surface of liquids (water in particular). This is because they possess another equally effective property of resisting any vertical displacement of their particles (or the property of maintaining a flat, free surface). Thus, water waves (ripples) are due to the effect of gravity, not elasticity. Gases do not have a free surface of their own and they do not resist any change in the shape. Thus, transverse wave motion is not possible in gases. |
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| In this type of wave motion, the individual particles of the medium vibrate parallel to the direction in which the wave travels. |
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| Example: The waves along the length of a spring when one end of it is suddenly compressed or pulled out and then released. |
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| Let a long coiled spiral spring be suspended horizontally from a wooden frame using a number of threads. Ordinarily, the turns of the spring will be equidistant. On giving a sharp tap to one end of the spring, a few turns will come closer together. This state of compression moves forward along the length of the spring. Similarly, if the end of the spring is sharply pulled out and released, the distance between the turns becomes greater than usual. This state of extension also travels along the length of the spring. If the end of the spring is alternately pushed in and pulled out, a series of compressions and elongations are found to travel along the length of the spring. The vibrations of the particles are horizontal and the wave propagation is also along the horizontal. Thus, it is a longitudinal wave. |
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| Let a stiff metallic strip (like a hacksaw blade) be fixed vertically on a rigid support. When its other end is pulled to one side and released, it begins to vibrate. The extreme positions of the vibrating strip are shown by dotted lines in the figure. As it suddenly moves to the right, it pushes the layers of air in front of it and causes a compression of air. This compression is then propagated onwards through the air. The strip while coming back, overshoots its equilibrium position and moves to the left causing a compression of the air layers on the left side while it creates a rarefied region on the right side. Both these conditions, namely compression and rarefaction move onwards in the medium as the strip vibrates. The vibrations of the particle are parallel to the wave propagation. Thus, it is a longitudinal wave. Such a wave does not require a shearing stress and hence, can pass through any medium possessing elasticity of volume (i.e., in solids, liquids or gases). |
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| In a liquid, the motion of the particles may be neither purely transverse nor purely longitudinal, but a combination of the two. The path followed by the particles is either a circle or an ellipse. The paths of several selected particles, their positions and the shape of the wave are shown in the figure. The particles move in circular paths if the wavelength is equal to or smaller than the depth of water. As the water becomes deeper, the path becomes elliptical and at the lower levels, the wave motion is entirely longitudinal. |
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| Comparison between transverse and longitudinal waves |
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