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Wave interactions

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**Describing waves A crest represents all the high points in a wave.**

A trough is all the low points in the wave.

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Representing waves The crest of a wave is sometimes called a wavefront. In these figures, wavefronts are shown in dark blue. Waves propagate in a direction perpendicular to their wavefronts. Animated illustration, page 418

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**Propagation To propagate is to spread out and grow.**

Waves propagate outwards from their source, carrying both energy and information. How do waves propagate?

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How do waves propagate? Waves propagate because of connections between the particles in the wave medium. A disturbance in one place causes a disturbance in the adjacent matter, such as in this water wave below. Demonstrate wave propagation with a Shive wave machine, if available.

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Reflection Reflection occurs for both longitudinal and transverse waves. Reflection causes a wave to change direction, and may also change its shape.

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Boundaries Reflection occurs at boundaries where conditions change—such as the edge of a pool or a wall in a room. The kind of reflection that occurs depends on whether the boundary is fixed or open.

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**Fixed boundaries A fixed boundary does NOT move in response to a wave.**

The wave pulse reflects on the opposite side of the spring. This behavior can be explained with Newton’s third law. The incoming pulse in the spring pulls UP on the wall, and the wall pulls DOWN on the spring.

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Open boundaries An open boundary allows the end of the spring to move freely. The wave reflects on the same side of the spring as the incident wave.

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Curved boundaries Curved boundaries alter both the shape and direction of a wavefront. They can turn plane waves into circular waves that converge at a point. They can also change the curvature of a circular wave.

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Refraction Refraction occurs when a wave changes speed at a boundary, resulting in a change of direction. Water waves refract if the depth changes. They refract because they move slower in shallow water than in deep water.

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**Refraction of a water wave**

A-B moves slower in shallow water. A-C moves slower in shallow water. Waves move fast in deep water. Shallow (slow) Waves on the open ocean will refract as they enter the shallow water near the shore of a beach or island. The refraction will bend the wave crests so that they come in more parallel to the shoreline.

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**Refraction and direction**

Refraction changes the direction of a wave.

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**Refraction and wavelength**

Refraction also changes the wavelength of a wave. Notice: as the wave slows down, its wavelength gets shorter.

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**Refraction and frequency**

Recall: When wave velocity changes during refraction, the wavelength also changes. But frequency CAN’T change: Every wave that enters the boundary must exit the boundary. Therefore, the number of waves per second must stay constant.

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All waves refract Refraction occurs for both transverse and longitudinal waves. Light waves are transverse waves. Light refracts when it changes speed passing from air to water. Sound waves are longitudinal waves. Sound refracts when it changes speed passing from cool air into warm air.

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Diffraction Diffraction is a property of waves that allows them to bend around obstacles and pass through gaps. Diffraction often changes the direction and shape of a wave.

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**Diffraction Longer wavelengths = more bending.**

When the wavelength is large compared to the gap, the waves diffract in complete arcs. When the wavelength is small relative to the gap, there is less diffraction and a larger “shadow zone”. This image on the right from the simulation reveals the single slit interference pattern. Students will not be ready to understand this pattern, but should be able to see the brighter central maxima and shadow zones to each side.

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**A paradox You are around the corner from a lamp and a speaker.**

Sound and light are both waves, and both can diffract. You can hear the speaker but not see the lamp. Why? you are here

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**Diffraction Longer wavelengths = more bending.**

Sound waves diffract around corners because sound waves have long wavelengths of centimeters to meters. Light waves also diffract, but their wavelength is much smaller (~10-5 cm), so the diffraction is imperceptibly small. Light casts sharp shadows.

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Interference

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**Multiple waves Examine this picture of the ocean.**

Notice that there are ripples on top of the waves. These ripples are actually smaller waves that are combining with larger waves. Waves of different amplitudes, wavelengths, and frequencies are often present at the same time. The sounds in a classroom are another example of waves of many different amplitudes, wavelengths, and frequencies are all present at the same time.

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Sine waves The simplest wave can be described by a single amplitude, wavelength, and frequency. These are referred to as sine waves.

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Sine waves The simplest wave can be described by a single amplitude, wavelength, and frequency. These are referred to as sine waves. Graphs of amplitude vs. position and amplitude vs. time can be modeled using the sine function.

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Sine waves The sine function repeats every cycle, or every 2π radians.

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**Sine waves The sine function repeats every cycle, or every 2π radians.**

What happens when two or more of these simple waves combine with each other?

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**Superposition principle**

The superposition principle says that the total amplitude at any point equals the sum of the amplitudes of all of the waves that occur at that same place and time.

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**Constructive interference**

When more than one wave is present, they can sum to make a larger or smaller amplitude wave. If the result is a larger amplitude wave, constructive interference has occurred.

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**Destructive interference**

Two waves can also add up to make a smaller wave. When two or more waves add up to make a smaller amplitude wave, destructive interference has occurred. If the amplitudes are exactly matched, there can be total destructive interference.

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**Interference and superposition**

In most real situations, many waves will be present. Some will interfere constructively; others will interfere destructively. The interference is often temporary, lasting only until the waves pass by each other.

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**Two opposite pulses start at opposite ends of this spring.**

Temporary interference Two opposite pulses start at opposite ends of this spring. Students can “mouse over” this illustration on page 426 to view the temporary interference depicted on these next three slides.

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**Two opposite pulses start at opposite ends of this spring.**

Temporary interference Two opposite pulses start at opposite ends of this spring. When they meet in the middle, they cancel.

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**Temporary interference**

Two opposite pulses start at opposite ends of this spring. When they meet in the middle, they cancel. They re-appear after passing through each other.

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**Resonance and standing waves**

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Standing waves Standing waves occur when a wave and its reflection interfere constructively. To make a standing wave, continuously launch wave pulses by shaking one end of a spring. If the rhythm is just right, each new pulse adds constructively to the reflection of the previous pulse.

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Nodes and antinodes A node is a stationary point where the amplitude stays zero.

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Nodes and antinodes An antinode is a point of maximum amplitude.

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**Standing waves and resonance**

Standing waves are a form of resonance. Resonance occurs when the size of a system matches some multiple of the wavelength. This standing wave has a wavelength equal to the size (length) of the system.

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**Natural frequencies At different frequencies, different standing wave**

patterns appear on a vibrating string. The fundamental is also called the first harmonic. The lowest frequency and longest wavelength wave is the fundamental.

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**Natural frequencies At different frequencies, different standing wave**

patterns appear on a vibrating string. The lowest frequency and longest wavelength wave is the fundamental. The next higher frequency wave is the second harmonic, at twice the frequency of the fundamental.

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Natural frequencies The third harmonic has three times the frequency of the fundamental, and so on. Each harmonic is a vibrating mode of the string. A mode is a characteristic pattern of vibration that occurs at a resonant frequency of the system. The natural frequencies of a system are the frequencies of its resonant modes.

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Homework / Classwork P 433 15.2 #6-12 15.3 #13-20

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