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Properties of Waves Chapter 12 Section 3

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What Is A Wave? Ripple waves in water are formed by the vibrations of water molecules. As the vibration waves spread outward to more molecules, the waves travel outward. A wave is considered to be the motion of disturbance. Particles within the wave vibrate around and equilibrium position.

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**Medium Medium – Material through which a disturbance travels.**

In order for a wave to form, it needs a medium which provides the particles that vibrate. The medium does not travel with the wave After the wave passes, the particles return to their equilibrium position. Examples: Sound: The medium is air Ocean Waves: The medium is water

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Mechanical Waves Mechanical Waves – A wave whose propagation requires the existence of a medium. Not all wave propagation requires a medium Electromagnetic waves

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**Wave Types Pulse Wave – A single non-periodic disturbance.**

A wave that consist of a single traveling pulse. Periodic Wave – A wave whose source is some form of periodic Motion. A wave that consist of multiple traveling pulses.

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Sine Waves If the source of the wave is in simple harmonic motion, then the wave mimics harmonic motion as well. A wave that is vibrating in simple harmonic motion is called a sine wave. A graph of a trigonometric function produces this curve when plotted. y = sin x

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Transverse Wave Transverse Wave – A wave whose particles vibrate perpendicular to the direction of wave motion. The particles vibrate up and down as the wave moves from left to right or vise versa. Examples: Electromagnetic waves Ocean waves Wave traveling through a rope

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Graphing Waveform – A waveform can represent either the displacements of each point of the wave at a single moment in time or the displacements of a single particle as time passes. Trigonometric function of sine represents the wave.

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**Graphing The x-axis represents the equilibrium position of the wave.**

The y-axis of the curve represents the displacement of each point on the wave at time (t).

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Describing a Wave Crest – The highest point above the equilibrium position. Trough – The lowest point below the equilibrium position. Wavelength – The distance between two adjacent similar points of the wave, such as crest to crest or trough to trough. Variable for wavelength – λ (Greek letter – Lamda) Amplitude – The point at which the displacement is its maximum distance away from the equilibrium position.

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**Transverse Wave Diagram**

y Wave Length Crest λ Amplitude Equilibrium Position Displacement x Amplitude Trough

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Longitudinal Waves Longitudinal Waves – A wave whose particles vibrate parallel to the direction of wave motion. The particles vibrate in the same direction as the direction of the wave. Often called density waves or pressure waves Crest are high density Trough are low density Examples: Sound Waves Earthquakes

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**Longitudinal Wave Diagram**

Stretched Compression Longitudinal Wave Density crest Equilibrium trough

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**Transverse Waves vs. Longitudinal Waves**

Transverse waves oscillate perpendicular to the direction of the wave propagation. Light Waves Longitudinal waves oscillate parallel to the direction of the wave propagation. Sound Waves Link: Transverse and Longitudinal Wave Animation

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Period and Frequency Frequency describes the number of crest or troughs that pass a given point in a unit of time. Period of a wave is the amount of time required for one complete vibration of particles or one wavelength.

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Speed of a Wave The speed of a wave can be found through the waves frequency and wavelength. The equation is derived through the linear kinematic equation for velocity.

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**Speed of a Wave Equation**

𝑣 = 𝑓𝜆 𝑣=𝑆𝑝𝑒𝑒𝑑 𝑜𝑓 𝑊𝑎𝑣𝑒 𝑚 𝑠 𝑓=𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝐻𝑧 𝜆=𝑊𝑎𝑣𝑒𝑙𝑒𝑛𝑔𝑡ℎ 𝑚 The speed of a mechanical wave remains constant for any given medium. If the frequency increases, the wavelength must decrease. Speed only changes if the medium changes.

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Example Problem A 2640 Hz whistle produces sound waves that have a wavelength of 50.0 cm in water. What is the speed of sound in the water?

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**Example Problem Answer**

v = 1320 m/s

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Energy and Waves The energy is transferred by the motion of the matter rather than by transferring matter itself. Energy is transferred very efficiently in a wave. Examples: Tsunamis Sound Earthquake Greater the amplitude, greater the energy

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