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## Wave Reflection and Standing Waves

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When a ball hits a hard wall, it is reflected by the wall. This reflection phenomenon can alternatively be interpreted in terms of the reflection of energy and momentum associated with the ball. If the wall is soft, the collision is inelastic and the wall completely absorbs the energy and momentum of the ball. No reflection occurs in this case. As we have seen, waves carry energy and momentum and whenever waves encounter an obstacle, they are reflected by the obstacle. Echoes are caused by the reflection of sound waves. Radars use the reflection of electromagnetic waves (microwaves) from metal objects such as airplanes. Wave reflection gives rise to an important wave phenomenon called standing waves, which play essential roles in most musical instruments. As the name indicates, standing waves do not propagate and therefore are not associated with energy and momentum transfer. They essentially behave as spatially distributed oscillators that only store energy. They can create waves in a surrounding medium by radiation. For example, the strings in a piano oscillate with distinct frequencies that are determined by the length, tension, and mass of each string. Each string can create sound waves in air with a particular frequency.

Chapter Contents:

• 6.1 Introduction
• 6.2 Reflection at a Fixed Boundary, Standing Waves
• 6.3 Reflection at a Free Boundary
• 6.4 Theory of Wave Reflection, Mechanical Impedance
• 6.5 Problems

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