Wave. 1. Transverse 2. Longitudinal 3. Standing

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Louise Baldwin
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Wave Wave: A disturbance traveling through a medium by which energy is transferred from one particle of the medium to another without causing any

) This characteristic of a wave as an energy transport phenomenon distinguishes waves from other types of phenomenon.

The wave medium is not the wave and it doesn't make the wave; it merely carries or transports the wave from its source to other locations.

In other words, the medium is composed of parts that are capable of interacting with each other.

1 Wave Wave: A disturbance traveling through a medium by which energy is transferred from one particle of the medium to another without causing any permanent displacementof the medium itself. (A Wave Transports Energy and Not Matter!) This characteristic of a wave as an energy transport phenomenon distinguishes waves from other types of phenomenon. Medium Medium:a substance or material that carries the wave. The wave medium is not the wave and it doesn't make the wave; it merely carries or transports the wave from its source to other locations. The news media as an example of a medium. Doesn t make news just transfers it. The medium is just a collection of interacting particles. In other words, the medium is composed of parts that are capable of interacting with each other. The interactions of one particle of the medium with the next adjacent particle allow the disturbance to travel through the medium. (Ex. slinky, air, water, sport fans, etc. Three types of waves: Categorized on the basis of the direction of movement of the individual particles of the medium relative to the direction that the waves travel. 1. Transverse 2. Longitudinal 3. Standing Transverse Wave Longitudinal Wave A wave in which particles of the medium move in a direction parallel to the direction that the wave moves. Compression Wave that vibrates perpendicular to the wave motion Requires a medium Rarefaction: reduction of a medium's density, or the (rair-uh-fak-shuhn) opposite of compression. 1

2 Standing Waves A standing wave is a wave that remains in a constant position. This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling in opposite directions. Standing Waves Are often observed in physical media such as strings and columns of air. Any waves traveling along the medium will reflect back when they reach the end. This effect is most noticeable in musical instruments where, at various multiples of a vibrating string or air column's natural frequency, a standing wave is created, allowing harmonics to be identified. Harmonics A harmonicof a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency, i.e. if the fundamental frequency is f, the harmonics have frequencies 2f, 3f, 4f,... etc. For example, if the fundamental frequency is 25 Hz, the frequencies of the harmonics are: 50 Hz, 75 Hz, 100Hz etc. Harmonics Fundamental 1 st harmonic 1 st overtone 2 nd harmonic 2 nd overtone 3 rd harmonic 3 rd overtone 4 th harmonic 4 th overtone 5 th harmonic 5 th overtone 6 th harmonic 6 th overtone 7 th harmonic Water Waves and Rayleigh Waves Are a combination of both transverse and longitudinal waves. Water waves occur in a liquid Rayleigh waves occur in a solid A type of surface acoustic wave that travels on solids. They are produced on the Earth by earthquakes. Waves in a solid vsa liquid Waves traveling through a solid medium can be either transverse waves or longitudinal waves. Waves traveling through the bulk of a fluid (such as a liquid or a gas) are always longitudinal waves. (except surface waves) Transverse waves require a relatively rigid medium in order to transmit their energy. As one particle begins to move it must be able to exert a pull on its nearest neighbor. 2

It is for this reason that only longitudinal waves are observed moving through the bulk of liquids such as our oceans.

3 Waves in a solid vsa liquid If the medium is not rigid as is the case with fluids, the particles will slide past each other. This sliding action that is characteristic of liquids and gases prevents one particle from displacing its neighbor in a direction perpendicular to the energy transport. It is for this reason that only longitudinal waves are observed moving through the bulk of liquids such as our oceans. Waves in a solid vsa liquid Earthquakes are capable of producing both transverse and longitudinal waves that travel through the solid structures of the Earth. When seismologists began to study earthquake waves they noticed that only longitudinal waves were capable of traveling through the core of the Earth. For this reason, geologists believe that the Earth's core consists of a liquid - most likely molten iron. Earthquake Waves The P waves (Primary waves) in an earthquake are examples of Longitudinal waves. The P waves travel with the fastest velocity and are the first to arrive. The S waves (Secondary waves) in an earthquake are examples of Transverse waves. S waves propagate with a velocity slower than P waves, arriving several seconds later. The Rayleigh waves in an earthquake are the waves that cause the most damage. They travel with velocities slower than S waves, and arrive later, but with much greater amplitudes. These are the waves that are most easily felt during an earthquake and involve both up-down and side-to-side motion. Surface waves in solids Can be both longitudinal and transverse in motion Rayleigh wave is a special type of surface wave in solids. The particles move in elliptical paths, with the major axis of the ellipse perpendicular to the surface of the solid. As the depth into the solid increases the "width" of the elliptical path decreases. Rayleigh waves are different from water waves in one important way the particles travel counter-clockwise. (In a water wave all particles travel in clockwise circles.) Rayleigh Wave Water Waves Longitudinal waves travel through waver at depth. However at the surface the waves are surface waves, which are truly a mixture of both longitudinal and transverse. The particles travel in clockwise circles. The radius of the circles decreases as the depth into the water increases. The movie below shows a water wave travelling from left to right in a region where the depth of the water is greater than the wavelength of the waves. 3

4 Crest Amplitude Trough The waves maximum displacement Depends on how wave was generated NOT velocity. Wavelength Distance between two repeating points The symbol for wavelength is λ The Greek letter lambda The number of complete oscillations it makes each second. Frequency is measured in Hertz Hz 1 Hz = 1 wave/second This is often said as cycles per second Period T (s) Frequency is closely related to period Number of oscillations per second f = 1 T T=time for one oscillation Only have for continuous waves!! 4

Velocity = wavelength Frequency v = λ f Practice Problems Pg 335 1-7 Measure speed of a wave using velocity (v)= d/t Wave Behavior What happens when waves cross

Reflection - Free End The energy and size of the pulse remains unchanged after the pulse is reflected or bounced back, the shape remains the same as the in-coming

5 Velocity = wavelength Frequency v = λ f Practice Problems Pg Measure speed of a wave using velocity (v)= d/t Wave Behavior What happens when waves cross boundaries? Incident Wave = Incoming Wave that hits the boundary Reflected Wave = Any portion of the wave that is sent back along its original path. Reflection - Free End The energy and size of the pulse remains unchanged after the pulse is reflected or bounced back, the shape remains the same as the in-coming pulse. Rigid Wall Boundary - Fixed End A boundary the wave cannot pass through The energy and the size of the pulse remains the same, however, the reflected pulse appears up side down. 5

Superposition of Waves Two waves exist at the same place at the same time Each affects the medium independently Principle of Superposition The displacement of a medium is equal to the sum of the

6 Superposition of Waves Two waves exist at the same place at the same time Each affects the medium independently Principle of Superposition The displacement of a medium is equal to the sum of the displacements of individual waves. Result of Superposition is called interference Constructive Interference Superposition of waves when wavelength is in the same direction. Wavelengths combine to make a new wave of a larger amplitude. The top of the new wave is called the anti-node Destructive Interference Superposition of waves when waves are in opposite direction Displacement will be zero if waves have equal but opposite amplitude Particles of the wave continue to move so waves will resume form Node is the location where waves cancel Noise Cancelling Headphones Microphone -A microphone placed inside the ear cup "listens" to external sounds that cannot be blocked passively. Noise-canceling circuitry - Electronics, also placed in the ear cup, sense the input from the microphone and generate a "fingerprint" of the noise, noting the frequency and amplitude of the incoming wave. Then they create a new wave that is 180 degrees out of phase with the waves associated with the noise. Speaker - The "anti-sound" created by the noise-canceling circuitry is fed into the headphones' speakers along with the normal audio; the anti-sound erases the noise by destructive interference, but does not affect the desired sound waves in the normal audio. Battery -The term "active" refers to the fact that energy must be added to the system to produce the noise-canceling effect. The source of that energy is a battery. Noise Cancelling Headphones 6

7 2 Dimensional Waves Waves do not always move straight towards a barrier. More often come at an angle Ray diagrams: Model waves movement Ray is drawn at a right angle to the crest of the wave Normal Line 2 Dimensional Waves Reflection Change in a wave s direction at a boundary. Law of Reflection The angle between the incident/normal and the reflected/normal are equal. Normal Line 2 Dimensional Waves Refraction Change in a waves direction at a boundary between two differentmedia. The velocity and wavelength change, but the frequency stays the same. Occurs when not reflected by, but transmitted through different medium. Normal Line Diffraction Waves able to go through or around a barrier, but only at a small point. Results in a curving of the wave Single Hole Diffraction Constructive and Destructive Interference occurs if wave is able to pass through multiple points of the barrier. Practice Problems Review 14.2 Wave Behavior pages Wave behavior review questions: Pg pg , 10, 14, 22, 31, 37, 40, 42, 43 7

Chapter 14: Waves. What s disturbing you?

Chapter 14: Waves. What s disturbing you? Chapter 14: Waves What s disturbing you? Wave Properties Waves carry energy through matter. The matter can move with the wave, or at right angles to it. Newton s laws and conservation laws govern the behavior