# Waves Definitions of Waves n A wave is

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Waves

Definitions of Waves n A wave is a traveling that carries through space and matter without transferring. n Transverse Wave: A wave in which the disturbance occurs to the direction of travel. • A type of transverse wave is n Longitudinal Wave: A wave in which the disturbance occurs to the direction of travel of the wave. • A type of longitudinal wave is n Surface Wave: A wave that has characteristics of both and waves.

Types of Waves n Mechanical Waves: Require a such as , , of a spring or the fabric of a rope. n Electromagnetic Waves: can travel in the absence of a medium.

Transverse Wave Characteristics n n n Crest: Trough: Amplitude: John Wiley & Sons . . (undisturbed position).

Transverse Wave Characteristics (cont. ) n Frequency(f): The number of the wave makes in n n The unit for frequency is Wavelength( ): The minimum at which the wave repeats the same pattern n n A single oscillation is also called a The units for wavelength are

Transverse Wave Characteristics (cont. ) n n Velocity (v): of the wave n Measured in n The formula to calculate the speed of a wave is Period (T): wave to complete one n n it takes for the The units for period is The formula to calculate the period is

Transverse vs. Longitudinal Waves

The the n of a wave is determined by in which it travels. That means that a given medium for • and inversely proportional. • As one Frequency n Relationships v = f Wavelength are , the other

The Inverse Relationships T= As the period the , . Frequency n Period

Speed of a Wave on a String n For a stretched rope or string: v= Where: n n n = Tension = linear density = As the tension , the speed As the mass , the speed This phenomena is commonly seen in . .

Waves at n Boundaries A wave incident upon a fixed boundary will have its reflected back in the opposite direction. Note that the wave pulse is after reflecting off the boundary. www. electron 4. phys. utk. edu

Interference n occurs whenever two waves occupy the same space at the same time. n Law of : When two or more waves are present at the same time at the same place, the disturbance is equal to the of the disturbances from the individual waves.

Wave Interference – Process by which two waves meet producing a net amplitude. www. electron 4. phys. utk. edu

Interference – Process by which two waves meet out each other. Wave

Waves n Wave: An interference pattern resulting from two waves moving in directions with the same and such that they develop a consistent repeating pattern of and interference.

Waves Node: The part of a standing wave where interference is at o out of phase). all times ( n Antinode: The part of the wave where interference is maximized ( ). n

Waves n n n When a wave impacts a boundary, some of the energy is , while some passes , or may be. The wave that passes through is called a wave. A wave that is transmitted through a boundary will lose some of its energy. n n Electromagnetic radiation will both down and have a wavelength when going into a denser media. Sound will when transitioning into a denser media.

Continuous Waves – Higher Speed to Lower Speed n Note the differences in wavelength and amplitude between of the wave in the two different mediums Transmitted Wave v 2 Displacement Incident + Reflected Wave -v 1 Boundary Higher speed Lower speed Longer wavelength Shorter wavelength Note: This phenomena is seen with light traveling from air to water.

The Wave Equation n waves can be represented by the following equation. y(x, t) = ymsin( t - x) Where: ym = = x= = t= n Note that the sum ( t degrees. - x) is in (2 / ) (2 f) , not

The Wave Equation y(x, t) = ymsin( t - n = 2 / Waveform repeats itself every n n x) . +x = 2 f Waveform travels through 1 (T) every. A phase constant ( ) can be included in the phase that represents all waves that do not pass through the origin.

The Wave Equation – An Alternate Representation y(x, t) = ymsin( t - x) n Substituting for (2 f), (2 / ) and ym (A) yields: or y(x, t) = Asin 2 (ft - 1 x) y(x, t) = Asin 2 (vt - x)

Key Ideas n n Waves transfer without transferring . Longitudinal waves like that of sound require a. Transverse waves such as electro-magnetic radiation (light) do not require a. In transverse waves, displacement is to the direction of the wave while in longitudinal waves, the displacement is.

Key Ideas n n Waves can with one another resulting in or interference. waves are a special case of constructive and destructive interference for two waves moving in opposite directions with the same , and.