Actualizar Secuencia Didactica: 3748

Actualizar Secuencia Didactica: 3748

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<p><b>EL UNIVERSO DE LAS ONDAS.</b></p><p><b></b></p><p>Una onda es una perturbación que se propaga en un medio. Constituye un espectaculo familiar el de las ondas producidas por la materia vibrante: Las ondas nos rodean por todas partes. Ondas sonoras, ondas luminosas, ondas hertzianas, etc. Son expresiones que pertenecen ya al lenguaje de todos los dias.</p><p><b>Las ondas son portadoras de energia. </b>Más no de materia.</p><p>¿Has estado cerca al sitio de una explosión? ¿Qué les ha sucedido a los cristales de puertas y ventanas de las edificaciones cercanas al lugar de la explosión? Se han roto sin necesidad de que hayan sido golpeados.</p><p>¿De que manera podemos explicar este comportamiento? Pues porque las ondas transfieren energia sin transferencia de materia.</p><p><b>Clases de ondas:</b></p><p><b></b></p><p>Las ondas de agua, las de sonido y las que se propagan en un resorte o en una cuerda, son ejemplos de <b>ondas mecánicas. </b>Para transportar su energía, las ondas mecánicas necesitan un medio material, como el agua, el aire , el resorte o la cuerda. Las leyes de Newton rigen el movimiento de estas ondas.</p><p>Las ondas de luz, las de radio y los rayos X, son ejemplos de <b>ondas electromagnéticas. </b>Éstas no requieren un medio para su movimiento, y viajan a través del espacio con la velocidad de la luz, 299,792,458 m/s. Sus características no pueden ser observadas directamente; por tanto se emplean las ondas mecánicas, cuyas propiedades se aprecian fácilmente, como modelo para estudiar el comportamiento de las ondas electromagnéticas en los capítulos siguientes.</p><p>Existe una tercera clase de ondas, las <b>materiales. </b>Los electrones y otras partículas muestran un comportamiento ondulatorio en ciertas condiciones. Para describir el comportamiento de las ondas materiales es indispensable la mecánica cuántica.</p><p>Las ondas mecánicas se dividen en tres tipos. Cada uno de elllos, perturba el medio de una forma diferente. Las <b>ondas transversales </b>hacen que las partículas del medio oscilen perpendicularmente a la dirección de propagación de la onda. La onda se mueve a lo largo del resorte hacia la derecha, pero el resorte mismo se mueve a lo largo del resorte hacia la derecha, pero el resorte mismo se desplaza hacia arriba y hacia abajo formando angulos rectos respecto al movimiento de la onda. Las ondas en plano y en las cuerdas de una guitarra son representativos de ondas transversales.</p><p>Una <b>onda longitudinal </b>hace que las particulas del medio se muevan paralelamente a la dirección de propagación de la onda. El desplazamiento del resorte está en la misma dirección del movimiento de la onda. El sonido es un ejemplo de una onda longitudinal.</p><p><br></p><p><br></p><p><img src="/web/uploads/6913/6302e5c7f6-captura.png"></p><br>

Ejercicios

<p style="text-align: center;"><img 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