P11 Waves 1 Basics.notebook December 13, 2013

Transcription

1 Ace Ventura Slinky Scene 1

2 Unit 4- Waves Waves are caused by vibrations, such as objects undergoing simple harmonic motion. Although water waves, sound waves, springs, and light all seem very different, they share many properties that can be explained using a wave model. This unit introduces trainees to some general wave properties which will later be appled to specific types of waves. 2

3 P11 Waves 1 Basics.notebook Waves Stadium Wave Surfing A wave is a disturbance that transfer energy. 3

4 A wave disturbance is created by a source. The source of a wave might be a rock thrown into water, your hand plucking a stretched string, or an oscillating speaker cone pushing on air. As a wave passes through a medium, the atoms that make up the medium are displaced from equilibrium. This is a disturbance of the medium. A wave transfers energy. The African Clawed Frog The African clawed frog detects prey animals by the vibrations they make in the water. They have an array of sensors called the lateral line organ on each side of its body. This organ detects oscillations of the water due to passing waves. The frog can determine where the waves come from and what type of animal made them, and whether a strike is called for. Dophins BATS 4

5 Types of Waves The vibration that creates a wave can be either: a wave pulse (a single vibration) a continuous or periodic wave (a vibration which repeats over time) Waves can be divided into two broad categories: Mechanical Waves these waves require a medium (some substance/material) in order to travel or move. Examples sound waves, water waves, slinky waves (air) (water) (slinky coils) Caution! Mechanical waves move through matter without actually carrying the matter with them. Electromagnetic Waves these waves do not require a medium in order to move (can travel in a vacuum); however, they can move through a medium if one is present. Mechanical waves cannot travel through a vacuum. Examples visible light, microwaves, x rays The Electromagnetic Spectrum Song 5

6 Direction of a Wave's Motion A wave can be defined in terms of the direction of the wave's motion compared to the direction of the medium's motion. Defining waves this way leads to three notable categories: transverse waves longitudinal waves surface waves Transverse Waves the particles of the medium vibrate perpendicular to the wave's direction of motion Animation courtesy of Dr. Dan Russell, Kettering University 6

7 Longitudinal Waves the particles of the medium move parallel to the wave's direction of motion Animation courtesy of Dr. Dan Russell, Kettering University Particle Movement Wave's Direction of Motion Water/Surface Waves the particles at the surface of the medium move in circles Animation courtesy of Dr. Dan Russell, Kettering University Water waves are an example of waves that involve a combination of both longitudinal and transverse motions. As a wave travels through the waver, the particles travel in clockwise circles. The radius of the circles decreases as the depth into the water increases. The movie above 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. Two particles in blue have been identified to show that each particle indeed travels in a clockwise circle as the wave passes. 7

8 Transverse Waves The high points of the wave are called crests and the low points are called troughs. The "middle" position is called the equilibrium or rest position. This is where the medium would lie if there was no wave passing through the medium. crest amplitude equilibrium position trough The maximum displacement of the wave from its equilibrium position is called the amplitude. The energy transported by a wave is directly proportional to the square of the amplitude. E α A 2 Tsunami (Indonesia 2004) 8

9 Longitudinal Pulses and Waves A region where the coils are pressed together in a small amount of space is known as a compression. A region where the coils are spread apart, thus maximizing the distance between coils, is known as a rarefaction. A wavelength, λ, is defined as the distance between the centers of successive compressions/rarefactions. 9

10 Wavelength (Van Morrison 1:16) The wavelength of a wave is often defined as the distance between two successive crests. Actually, it is the distance between any two successive points where the wave motion repeats. λ λ λ Wavelength is given the symbol λ (called lambda) and is measured in meters. 10

11 Wave Terminology 11

12 Frequency The frequency is the number of complete wave cycles that pass a given point per unit time. Frequency is given the symbol f and is measured in hertz. Pitch Frequency of Sound Waves Colin's Lab Cymatics Note The frequency of a wave does not depend on the medium through which the wave is passing. The frequency of wave depends only on the frequency of the source of vibation! Period Closely related to frequency is the measurement called period. The period of a wave is the time needed for the wave motion to repeat. The symbol T represents period, which is measured in seconds. 12

13 Example A child swings back and forth on a swing 15 times in 30.0 s. Determine the frequency and period of the swing. 13

14 Speed The wave speed is the speed at which any part of the wave moves. It is not the speed of the particles of the medium. If we replace the period with 1/f, we get a new formula for wave speed. f frequency Hz λ wavelength m v speed m/s This equation is known as the wave equation and it applies to ALL the wave types. Note Unless otherwise stated, you can assume that electromagnetic waves travel at a speed of 3.00 x 10 8 m/s (the speed of light in a vacuum). The following are all electromangetic waves. radio waves microwaves infrared waves visible light ultraviolet waves x rays gamma rays 14

15 NOTE The speed of a wave depends only on the nature/ properties of the medium that it is passing through. When a wave moves from one medium to another, the frequency remains the same but the speed changes. Examples Water waves change their speed depending on the depth of the water. As waves move from deep to shallow water, their wavelengths decrease. Therefore, waves travel slower in shallower water. A Slinky Dog is stretched out between Bubba and Figgy Newton. Bubba sends a pulse down the Slinky Dog. If Bubba and Figgy back away from one another, the Slinky Dog will stretch out even more. This essentially changes the medium. If Bubba sends another pulse down the Slinky Dog, the pulse will travel at a greater speed. 15

16 Example 1 A hiker shouts toward a vertical cliff 685 m away. The echo is heard 4.00 s later. The wavelength of the sound is m. a. What is the speed of sound in air? b. What is the frequency? c. What is the period of the wave? The speed of sound in air is 343 m/s. The frequency is 457 Hz. The period of the wave is 2.19 x 10 3 seconds. 16

17 Check Your Understanding Water waves in a lake travel 4.4 m in 1.8 s. the period is 1.2 s. What is the speed and wavelength of the water waves? The speed of the water wave is 2.4 m/s and the wavelength of the water wave is 2.9 meters. 17

18 The Slinky Pledge I promise to be kind to all Slinkies. I will not exceed the elastic limit of any Slinky under my care. I will not allow Slinkies under my care to "co mingle." The cost of one Slinky $3.98 (not including tax). A Happy Slinky priceless. 18

19 Slinky P MOV Commercial "It's Slinky" (early 1960s) Commercial "It's Slinky" (1960s) Commercial "It's Slinky" (1980s) 19

20 Check Your Learning The of a wave depends only on the medium in which it is travelling. a. Frequency b. Period c. Speed d. Wavelength c.speed When a wave passes from one medium to another, the must stay the same. a. Amplitude b. Frequency c. Speed d. Wavelength b) frequency 20

21 Check Your Learning A wave in which the medium moves parallel to the medium is called a wave. a. Electromagnetic b. Longitudinal c. Mechanical d. Transverse b) longitudinal The vertical distance from top of a crest to the bottom of a trough is 34.0 cm. The amplitude of this wave is a. 8.5 cm b cm c cm d cm b) 17 cm. 21

22 A wave has a period of 0.20 s. What is the frequency? a Hz b. 1.0 Hz c. 5.0 Hz d. 20. Hz c) 5.0 Hz Check Your Learning 22

23 Wave Behaviors The Law of Reflection When a wave strikes a boundary at an angle, the wave will bounce off the boundary at the same angle. The blue and purple lines represent wave fronts. They represent the crests of the waves. A better way to show the motion of a wave is to draw lines called rays. The normal is a line that is perpendicular to the boundary. It is a useful reference for measuring angles. The angle between the normal and the inicident ray, θ i, is called the incident angle. The angle between the normal and the reflected ray, θ r, is called the reflected angle. The Law of Reflection θ i = θ r The angles must be measured from the normal to the rays and NOT from the boundary to the ray. 23

24 Refraction When a wave crosses into a new medium where its speed is different, it will change its direction of motion. This phenomenon is known as refraction. More about this wave behavior a little later... 24

25 Diffraction When waves encounter a barrier they tend to bend around it and spread into the area behind the obstacle. This phenomena is called diffraction. You may have noticed diffraction as water waves hit a pier or buoy. Waves may also be diffracted by an aperture (an opening in a barrier). The amount of diffraction depends on: 1. the size of the opening; the smaller the opening the greater the diffraction. 2. the wavelength; the longer the wavelength, the greater the diffraction. Refelection, Refraction and Diffraction 25

26 The Principle of Superposition "When two or more waves are simultaneously present at a single point in space, the displacement of the medium at that point is the sum of the displacements due to each individual wave." Simulation Superposition of Waves The supersposition of two waves is often called interference. The displacement of the medium where the waves overlap is larger than it would be due to either of the waves separately. The displacement of the medium where the waves overlap is less than it would be due to either of the waves separately. The term phase is used to describe the relative positions of the crests of two different waves. waves are said to be "in phase" when the crests are aligned. waves are said to be "out of phase" when the crests do not line up. 26

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28 Check Your Understanding The process by which a wave bounces off an obstacle in its path us called a. Diffraction b. Reflection c. Refraction d. Superposition b) reflection The bending of waves as they go from one medium to a new medium is called a. Diffraction b. Reflection c. Refraction d. Superposition c) Refraction 28

29 Standing Waves If two interfering waves have just the right frequency, the same wavelengths and equal amplitudes, a special wave called a standing wave will be produced. They are called standing waves because although the medium moves, there does not appear to be any propogation of the wave. Simulation Standing Waves antinode node Standing waves have alternating nodes and antinodes. node: a point in the medium that is completely undisturbed at all times (at this point the medium is never displaced); it is produced by the destructive interference of waves antinode: a point in the medium that undergoes the greatest displacement; it is produced by the constructive interference of waves The smallest frequency that will produce a standing wave is called the fundamental frequency. A more complicatedf standing wave whose frequency is twice that of the fundamental frequency. The distance between nodes/antinodes is 1λ. 2 29

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31 Standing Waves.MOV Standing Waves 2.MOV 31

32 Sample Problem The distance between adjacent nodes in a vibrating string is 15 cm. What is the wavelength of the standing wave? λ The wavelength of the standing wave is 45 cm. 32

33 Sample Problem A standing wave with a frequency of 45.0 Hz is produced in a string. The distance between the second node and the fifth node is 36 cm. What is the wavelength of the wave? 33

34 Resonance The natural frequency is the lowest frequency at which an object will vibrate when it is allowed to vibrate freely. Resonance is a phenomena that occurs when energy is added to a vibrating system at the same frequency as its natural frequency; during resonance, the amplitudes of the vibrations of the object become larger. Examples 1. Shattering Glass 2. Tacoma Narrows Bridge 3. Rice 34

35 P11 Waves 1 Basics.notebook Breaking a Wine Glass using Resonance 35

36 Tacoma Narrows Bridge On November 7, 1940, at approximately 11:00 AM, the Tacoma Narrows suspension bridge collapsed due to wind induced vibrations. Situated on the Tacoma Narros in Puget Sound, near the city of Tacoma, Washington, the bridge had only been open for traffic for a few months. (Bridge Collapse) (Rice and Resonance) (MRI) 36

37 Wave Behaviors Speed The speed of a wave depends only on the properties of the medium that it is passing through. This is true for both mechanical and electromagnetic waves. When waves pass into a new medium, their speed will either increase or decrease. Wave pulses travel slower in large, heavy springs. A heavy spring can be referred to as a 'slow medium". Pulses travel faster in small, lighter springs. A light spring can be referred to as a "fast medium". Frequency Two ropes are tied together. What will be the frequency of the wave in the new medium? Period What happens to the period of a wave as it passes from one medium into another? Wavelength What happens to the length of a wave as it passes from one medium into another? Amplitude What happens to the amplitude of a wave as it passes from one medium into another? 37

38 BOUNDARY BEHAVIOR The behavior of a wave (or pulse) upon reaching the end of a medium is referred to as boundary behavior. When a pulse/wave encounters a different medium only a portion of the pulse/wave will enter the new medium. Some of the initial pulse/wave energy will "bounce back" and remain in the initial medium. This phenomenon is known as reflection. The diagram shows that the amplitude doesn't change when the pulse reflects, but the pulse is inverted. We can understand why by looking at the forces at the boundary. When the pulse reaches the wall, the piece of string right at the wall feels an upward force from the approaching pulse. But this piece of string is fixed in place, so there must be an opposite force from the wall on this piece of string. This downward force leads to an inverted reflected pulse. 38

39 Three Important Waves The initial wave is called the incident wave. The portion of the wave that enters the second medium is called the transmitted wave. The portion that is reflected back into the first medium is called the reflected wave. Boundary Boundary 39

40 The degree of difference between the two mediums determines how much of the incident wave is reflected. Examples If the mediums are very similar (fresh and water and salt water), most of the incident wave will be transmitted. If the mediums are very different (water and molasses) most of the incident wave will be reflected. 40

41 Check Your Learning A pulse goes into a medium that is less dense. The reflected pulse is a. Faster b. Inverted c. Larger d. Upright d) upright Resonance occurs when one object causes a second object to vibrate. The second object must have the same natural a. Amplitude b. Frequency c. Speed d. Wavelength b) frequency 41

42 Attachments Van Morrison Wavelength