 # When an object moves back and forth, it is called a vibration

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When an object moves back and forth, it is called a vibration
When an object moves back and forth, it is called a vibration. Vibrations carry energy.

Wave - a disturbance that propagates through a medium or space

Waves are a method of transporting energy.

A wave involves some quantity or disturbance that changes in magnitude with respect to time at a given location and changes in magnitude from place to place at a given time.

Some waves require a material medium for their propagation
Some waves require a material medium for their propagation. These waves are called mechanical waves.

A single, nonrepeating disturbance is called a pulse wave.

If the motion responsible for the wave disturbance is periodic, a periodic wave, or wave train, is produced.

This wave motion is related to simple harmonic motion, but instead of one object vibrating about its equilibrium position, many particles do so.

Waves provide a mechanism by which energy is transmitted from one location to another without the physical transfer of matter between these locations.

A mechanical wave is a disturbance in the equilibrium positions of matter, the magnitude of which is dependent on location and on time.

This requires a source of energy and an elastic medium.

Periodic Waves - each individual particle repeats its motion once every certain time interval T, which is called the period of vibration. (Same as the pendulum)

The frequency of a periodic wave is the number of waves passing a given point in unit time.

Frequency is the number of cycles per unit time
Frequency is the number of cycles per unit time. The SI unit is the hertz (Hz). One hertz is one cycle per second. A “cycle” is an event, not a unit, so the dimension of one hertz is s-1.

The period, T, of a wave is the time between the passage of two successive crests past a given point. Period is the reciprocal of frequency. f = 1/ T and T = 1/ f

The wavelength, l (lambda), is the distance between any particle and the next particle that is in phase with it.

One wavelength is the distance advanced by the wave in one period, T.

Middle C is 264 Hz. If the speed of sound is 343 m/s, find the wavelength of the sound.

The Sears Building in Chicago sways back and forth at a frequency of about 0.1 Hz. What is its period of vibration?

The speed, v, of a wave depends on the nature of the wave and the medium through which it passes. v = f l

If a water wave vibrates up and down two times each second and the distance between wave crests is 1.5 m, what is the frequency of the wave? What is its wavelength? What is its speed?

What is the wavelength of a 340-Hz sound wave when the speed of sound in air is 340 m/s?

What is the frequency of your favorite radio station? What is its wavelength?

Maximum displacement from equilibrium is amplitude and is a measure of energy flow.

Energy transported by a wave per unit time is the power of the wave.

The rate of transfer of energy, or the power transmitted by a wave system, is proportional to the square of the wave amplitude and also to the square of the wave frequency.

In other words, if the amplitude or frequency is doubled, the vibrational energy is increased fourfold.

Expanding water ripples must maintain the total energy, so the amplitude of the wave must decrease as the circles expand.

This effect is greater for sound waves because the waves are expanding spheres.

Damping is the reduction in amplitude of a wave due to the dissipation of wave energy as it travels.

The two basic types of waves are transverse and longitudinal.

Transverse wave - the displacement of the particles of the medium is perpendicular to the direction of propagation of the wave.

An upward displacement is called a crest
An upward displacement is called a crest. A downward displacement is a trough.

Longitudinal wave – the displacement of particles of the medium is parallel to the direction of propagation of the wave.

Compressions - areas where particles are closer together than normal.

Rarefactions - areas where particles are farther apart than normal.

Water waves are not really either longitudinal or transverse
Water waves are not really either longitudinal or transverse. The individual particles of water actually move in a circular motion.

Many waves can pass through a medium at one time.

Each wave proceeds independently as if the other waves were not present.

Superposition - the action of each wave on a particle is independent of the action of the other, and the particle displacement is the resultant of both wave actions.

Superposition Principle When two or more waves travel simultaneously through the same medium, (1) each wave proceeds independently as though no other waves were present and:

(2) the resultant displacement of any particle at a given time is the vector sum of the displacements that the individual waves acting alone would give it.

Interference - the effects produced by two or more waves superposing
Interference - the effects produced by two or more waves superposing. (especially waves of the same frequency)

Same frequency, in phase: constructive interference, increases amplitude.

Same frequency, 180° out of phase: destructive interference, decreases amplitude.

There can be interference where some areas constructively interfere and some areas destructively interfere.

This is called an interference pattern.

Points of zero displacement are called nodes
Points of zero displacement are called nodes. The lines along which they occur are called nodal lines.

Points of maximum displacement are called antinodes (or loops)
Points of maximum displacement are called antinodes (or loops). The lines along which they occur are called antinodal lines.

The total energy of the two wave systems remains unchanged, but the energy distribution from the interference is different.

A standing wave – a wave produced by the interference of two periodic waves of the same amplitude and wavelength traveling in opposite directions.

The nodes have no amplitude; between the nodes, the loops have maximum amplitude.

A wave is reflected when it encounters a barrier that is the boundary of the medium in which the wave is traveling.

Law of reflection - angle of incidence is equal to the angle of reflection.

A boundary that allows unrestrained displacement of the particles of a medium reflects waves with no change in the direction of the displacement (no change in phase).

Reflection at the fixed termination of a medium occurs with a reversal of the direction of the displacement (180° phase shift).

Reflection: free-end termination- no phase change
Reflection: free-end termination- no phase change. fixed-end termination- inverted phase.

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