AP1200_Ch3_Waves-2008 - AP1200 Foundation Physics Limited...

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AP1200 Foundation Physics Limited wisdom and incorrect predictions: "The wireless music box has no imaginable commercial value. Who would pay for a message sent to nobody in particular?" -- David Sarnoff's associates in response to his urgings for investment in the radio in the 1920s. "We don't like their sound, and guitar music is on the way out." -- Decca Recording Co. rejecting the Beatles, 1962. Chapter 3: Waves There are two main types of waves; mechanical waves and electromagnetic waves. Mechanical waves – involve the disturbance of some physical medium, e.g. sound waves in air, vibrations on a string, and waves in water. Electromagnetic waves – do not require a medium to propagate, e.g. light, radio waves, and x-rays. We will consider mechanical waves first, then electromagnetic waves. 3.1 Propagation of a Wave Consider a ball floating in water. If a stone is thrown into the water some distance away, waves will be generated that propagate radially outwards. When the waves reach the ball, they will cause the ball to oscillate up and down, and from side to side but there is no net displacement of the ball. The small elements of water behave in the same way. The water waves travel away from the origin of the stone but the water itself is not carried by the wave. The waves have caused the ball to move so energy must be transported by the wave, but matter is not . This is a central feature of wave motion. One way to demonstrate a wave is to flick one end of a long rope (Fig. 3.1). The pulse generated will travel along the string with a definite speed, v . Each part of the string, point P for example, is disturbed in a direction perpendicular to the direction of travel of the pulse. No part of the string moves in a direction parallel to the string. This is called a transverse wave . A compression wave travelling along a spring (Fig. 3.2) is an example of a longitudinal wave . In this case, elements of the medium oscillate in a direction parallel to the direction of wave propagation. There is no movement in the transverse direction. An example of a longitudinal wave is sound waves. Sound causes longitudinal pressure fluctuations that propagate through the air. 1
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P P P Fig. 3.1 A pulse travelling along a string stretched compressed compressed stretched Fig. 3.2 A longitudinal wave in a spring Some waves have both transverse and longitudinal components, such as waves from an earthquake and waves on the surface of water. Consider again a pulse travelling along a string (Fig. 3.3). The shape of the wave does not change as the wave propagates along the string. At time t =0, we can represent the shape of the pulse by some mathematical function, ( ) ( ) x f x y = 0 , . This function describes the transverse displacement y , of each point along the string. P y x P vt y x a) time t = 0 b) pulse at time t Fig. 3.3 Pulse travelling along a string At some later time, t , the pulse will have travelled a distance vt to the right. Consequently, the element of the string at position x will then have the same displacement as the element at position vt x had at time 0 = t .
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This note was uploaded on 04/17/2011 for the course AP 1200 taught by Professor Michela.vanhove during the Spring '10 term at City University of Hong Kong.

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AP1200_Ch3_Waves-2008 - AP1200 Foundation Physics Limited...

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