#### Oscillation and Waves, Physics tutorial

Introduction:

Waves are present all over the place. Whether we identify it or not, we come across waves on the daily basis. Visible light waves, Sound waves, microwaves, stadium waves, water waves, radio waves, sine waves, earthquake waves, cosine waves, waves on the string, and slinky waves and are just a few of cases of daily encounters with waves. In addition to waves, there are the varieties of phenomena in physical world which look like waves so closely which we can explain such phenomenon as being wavelike. Motion of the pendulum, motion of the mass suspended by the spring, motion of the child on swing can be thought of as wavelike phenomena.

Physics of waves gives a rich sight in physical world which we look to understand and explain as students of physics. Before starting the formal discussion of nature of waves, it is frequently helpful to think about different encounters and exposures which we have of waves.

Waves are generated by some form of the disturbance, like the rock thrown in water, a duck shaking its tail in water or the boat moving through water. Water wave has the crest and trough and travels from one place to another. One crest is frequently followed by the second crest which is frequently followed by the third crest. Every crest is separated by the trough to make the alternating pattern of crests and troughs.

The waves may seem to be plane waves which travel together as the front in the straight-line direction, may be towards the sandy shore. Or waves may be circular waves which originate from point where disturbances take place; such circular waves travel across surface of water in every directions.

Medium:

The medium is substance or material which carries wave. The wave medium is substance which carries the wave (or disturbance) from one place to another. Wave medium isn't wave and it does not make wave; it just carries or transports wave from source to other places. In case of slinky wave, medium through that wave travels is slinky coils. In the case of the water wave in the ocean, the medium by which wave travels is ocean water. In case of the sound wave moving from church choir to the pews, the medium by which sound wave travels is air in room. And in the case of stadium wave, the medium by which stadium wave travels is fans which are in the stadium.

Categories of Waves:

One method to classify waves is on basis of direction of movement of the individual particles of medium relative to the direction that the waves travel. Classifying waves on this basis leads to three distinguished categories: transverse waves, longitudinal waves, and surface waves.

Transverse wave:

The transverse wave is the wave in which particles of medium move in the direction perpendicular to direction that the wave moves. Assume that slinky is stretched out in horizontal direction across classroom and that the pulse is introduced in slinky on left end by vibrating first coil up and down. Energy will start to be transported through slinky from left to right. As energy is transported from left to right, individual coils of medium will be displaced upwards and downwards. In this situation particles of medium move perpendicular to direction that pulse moves. This kind of wave is the transverse wave. Transverse waves are always classified by particle motion being perpendicular to wave motion.

Longitudinal wave:

The longitudinal wave is the wave in which particles of medium move in the direction parallel to direction that wave moves. Assume that slinky is stretched out in the horizontal direction across classroom and that the pulse is introduced in slinky on left end by vibrating first coil left and right. Energy will start to be transported through slinky from left to right. As energy is transported from left to right, individual coils of the medium will be displaced leftwards and rightwards. In this situation, the particles of medium move parallel to direction that pulse moves. This kind of wave is longitudinal wave. Longitudinal waves are always classified by particle motion being parallel to wave motion.

Sound wave:

A sound wave traveling through air is the classic example of the longitudinal wave. As the sound wave moves from lips of the speaker to the ear of the listener, particles of air vibrate backward and forward in same direction and opposite direction of energy transport. Every individual particle pushes on neighboring particle so as to push it forward. Collision of particle 1 with neighbor serves to restore particle 1 to original position and displace particle 2 in the forward direction. This back and forth motion of particles in direction of energy transport creates regions inside medium where particles are pressed together and other regions where particles are spread apart. Longitudinal waves can always be rapidly recognized by presence of such regions. This procedure continues along chain of particles until the sound wave reaches ear of the listener.

Oscillation:

Oscillation, in general, is the periodic fluctuation between two things; in broadest sense, oscillation can take place in anything from the person's decision-making procedure to tides and pendulum of the clock. Oscillation in the device known as oscillator is generally a back and forth motion over the central neutral point, developed by changes in energy. In the pendulum-driven clock, for instance, oscillation is back and forth movement of pendulum. Oscillators may be mechanical or electronic, but all work on same principles. Other devices based on principles of oscillation comprise oscillograph and oscilloscope.

Like other oscillators, clock pendulum's oscillation is kept by changes in energy. In this situation, potential energy , present when pendulum is at the top of swing, is converted to kinetic energy as pendulum falls and is driven upwards on other side. When kinetic energy has been spent, at top of swing, the pendulum's energy is potential yet again. With no kinetic energy to drive it higher, pendulum falls. The pendulum clock keeps time according to frequency of pendulum's swing (number of times it swings per second). Friction would finally cause movement to stop, but mechanical pendulum clocks use spring to help device conquer friction's drag. Many modern timepieces utilize quartz or electronic oscillators. Most accurate timepiece in world, the atomic clock estimate time according to oscillation within atom s.

Harmonic oscillator:

The harmonic oscillator is the system in physics which acts according to Hooke's law. This rule explains elastic behavior, and puts forth that amount of force applied to the spring, or other elastic object, is proportional to displacement. The harmonic oscillator system returns to original position when force is removed from elastic object.

In physics courses, simple example of the block attached to the wall by the spring is frequently utilized to show concept of harmonic oscillation. Surface that block slides on is supposed to be frictionless. When system is set in motion, it follows equation ω0 = 2πf0, that is also equal to square root of spring constant (k), divided by mass of block (m).

ω0 is angular speed, that has units of radians per second, and f0 is natural frequency, that has units of Hertz. Period of the block -time it takes to go through one complete cycle of motion - is equal to one divided by f0. Spring constant indicates how stiff spring is, and is unique to every spring. It has units of force per length, for instance, Newtons per meter.

This simple example is known as undamped harmonic oscillator, and, theorizes that as block moves along the frictionless surface, it will carry on moving at same frequency forever. In reality, though, such a case would not take place. Real systems with friction are known as damped systems, in which motion of the block will slow down, displacement of the spring will become shorter, and system will ultimately stop moving.

The harmonic oscillator system may be overdamped, underdamped, or critically damped. Differential equations explain motion of damped systems, so their solution can be fairly complex. Every kind of damped system has its own kind of motion, though, which is simply identifiable.

The quantum harmonic oscillator explains how two molecules interact with one another. They vibrate backward and forward in the similar manner to the mass on the spring. Instead of spring constant, equation for the quantum harmonic oscillator utilizes bond force constant that explains strength of bond between two molecules. Relationship between angular speed and frequency is the same.

Each hand of the clock comes back to given position after lapse of the certain time. This is a well-known example of periodic motion. When the body in periodic motion moves to and- fro (or back and forth) about its position, motion is known as vibratory or oscillatory.

Oscillatory motion is the common phenomenon. Familiar examples of oscillatory motion are:

The oscillating bob of the pendulum clock, piston of engine, vibrating strings of the musical instrument, oscillating uranium nucleus before it fissions, even large scale buildings and bridges may sometimes suffer oscillatory motion. Several stars show periodic variations in brightness). Such oscillations, left to themselves, don't continue indefinitely, i.e., they slowly die down because of different damping factors like friction and air resistance, etc. Therefore, in real practice, oscillatory motion may be fairly complex, as for example, vibrations of the violin string.

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