Progressive Wave vs Stationary Wave
Waves are a very important phenomena occurring in real life. The study of waves and vibrations runs a long way back in time. The concepts of stationary waves and progressive waves are discussed in many fields of physics and chemistry. These are discussed in mechanics, acoustics, radar technology, communication technology, quantum mechanics and even music. It is vital to have a proper understanding in progressive waves and stationary waves in order to excel in such fields. In this article, we are going to discuss what are stationary waves and progressive waves, their definitions, the similarities between stationary waves and progressive waves, how progressive waves and stationary waves are produced, their applications and finally the difference between stationary waves and progressive waves.
Progressive Waves
A mechanical wave is caused by any turbulence in a medium. Simple examples for mechanical waves are sound, earthquakes, ocean waves. A wave is a method of energy propagation. The energy created in the turbulence is propagated by the waves. A sinusoidal wave is a wave which oscillates according to the equation y = A sin (ωt – kx). As the wave propagates through the space, the energy it carries is also propagated. This energy causes the particles on the way to oscillate. It can also be interpreted the other way around as the energy is propagated through the oscillation of particles. There are two types of progressive waves; namely, longitudinal waves and transverse waves. In a longitudinal wave, the oscillations of particles are parallel to the direction of propagation. This does not mean the particles are moving with the wave. The particles only oscillate about fixed equilibrium point in space. In transverse waves, the oscillation of particles occurs perpendicular to the direction of propagation. Sound waves consist of only longitudinal waves, waves on a string is transverse. The ocean waves are a combination of transverse waves and longitudinal waves.
Stationary Waves
Stationary waves, which are also known as standing waves, occur due to the interception two identical waves travelling in opposite directions. Two identical sinusoidal waves travelling in +x and –x directions can be represented by y_{1} = A sin (ωt – kx) and y_{2} = A sin (ωt + kx) respectively. The addition of these two equations gives the superimposition of the two waves. Therefore y_{1}+y_{2} = y = A [sin (ωt – kx) + sin (ωt + kx)]. By simplifying this equation, we get Y = 2A sin (ωt) cos (kx). For a given x value, the equation becomes Y = B sin (ωt), the simple harmonic oscillation.
What is the difference between Progressive and Stationary Waves? • Progressive waves carry a net amount of energy through the path of the wave. A stationary wave does not carry a net energy through the path. • Two identical propagating waves are required to create a stationary wave. • The amplitude of a stationary wave changes over distance but for a given point, the amplitude remains fixed. The amplitude of each and every point of a propagating wave is the same, given that the wave is uniform.

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