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Vibrations & Waves Chapter 25 - This will be phun!

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Presentation on theme: "Vibrations & Waves Chapter 25 - This will be phun!"— Presentation transcript:

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2 Vibrations & Waves Chapter 25 - This will be phun! Vibrations & Waves Chapter 25 - This will be phun!

3 2 Types of Waves Mechanical Wave: Requires a mechanical medium Sound, water, air, springs, or ropes are examples. Electromagnetic Waves (EM): Does not require a medium for motion to occur Light, Radio, and X-rays are examples. 2 Types of Waves Mechanical Wave: Requires a mechanical medium Sound, water, air, springs, or ropes are examples.

4 “Making Waves” Making Waves

5 Transverse Waves Causes the particles of the medium to vibrate perpendicularly to the direction of motion of the wave. Piano and guitar strings are examples Transverse Waves Causes the particles of the medium to vibrate perpendicularly to the direction of motion of the wave.

6 Longitudinal Waves When particles of the medium move parallel to the direction of the waves. Fluids, liquids, gases, or plasma usually transmit only longitudinal waves. Longitudinal Waves When particles of the medium move parallel to the direction of the waves.

7 Longitudinal and Transverse Longitudinal and Transverse

8 Longitudinal vs Transverse Waves Compression = Crest Rarefaction = Trough Energy Movement: parallel vs perpendicular Wavelength: compression + rarefaction crest + trough Longitudinal vs Transverse Waves Compression = Crest Rarefaction = Trough Energy Movement: parallel vs perpendicular Wavelength: compression + rarefaction crest + trough

9 Surface Waves They are a mixture of transverse and longitudinal waves. (water & Rayleigh) The particles move both parallel and perpendicular to the direction of the wave. Surface Waves They are a mixture of transverse and longitudinal waves.

10 Wave Pulse and Traveling Wave Wave Pulse: A single disturbance that travels through a medium. Traveling Wave: Moving, periodic disturbances in a medium or field. Wave Pulse and Traveling Wave Wave Pulse: A single disturbance that travels through a medium.

11 Period The shortest time interval during which the motion repeats itself. Abbreviated with the capital letter,T SI Unit: seconds (s) Period The shortest time interval during which the motion repeats itself.

12 Frequency The number of complete revolutions per second. Frequency is abbreviated with a fancy ƒ. Frequency is measured in Hertz, Hz. A Hertz is one vibration per second (1/s). Frequency The number of complete revolutions per second.

13 Equation Frequency and the period of a wave are related by the following equation. Frequency and Period are reciprocals of each other. Equation Frequency and the period of a wave are related by the following equation.

14 Wavelength The shortest distance between points where the wave pattern repeats itself. The wavelength is abbreviated with the Greek letter, lambda, A: ? B: ? C: ? D: ? E: ? Wavelength The shortest distance between points where the wave pattern repeats itself.

15 Wavelength The shortest distance between points where the wave pattern repeats itself. The wavelength is abbreviated with the Greek letter, lambda, A: 1 Wavelength B: 2X Amplitude C: Nodes D: Amplitude E: ½ Wavelength Wavelength The shortest distance between points where the wave pattern repeats itself.

16 Vocabulary Crests: The high points of each wave motion. Troughs: The low points of each wave motion Amplitude: The maximum displacement from the rest or equilibrium position. Nodes: Where the wave crosses the equilibrium line. Antinodes: The bottom of the trough and the top of the crest Vocabulary Crests: The high points of each wave motion.

17 Vocabulary Crests: The high points of each wave motion. Troughs: The low points of each wave motion Amplitude: The maximum displacement from the rest or equilibrium position. Nodes: Where the wave crosses the equilibrium line. Antinodes: The bottom of the trough and the top of the crest A&F: Crests (Antinodes) D&I: Troughs (Antinodes) B,E,G,J: Nodes Vocabulary Crests: The high points of each wave motion.

18 To find the velocity of a wave Wave velocity (v) is the product of the frequency (f) and wavelength ( ). To find out how fast a wave moves, you would use this equation… To find the velocity of a wave Wave velocity (v) is the product of the frequency (f) and wavelength ( ).

19 Amplitude and Energy In order to produce a wave with a larger amplitude, more energy is needed. Waves with larger amplitudes transfer more energy. Amplitude does not affect frequency nor velocity. Amplitude and Energy In order to produce a wave with a larger amplitude, more energy is needed.

20 Waves Changing Mediums Waves passing from one medium to another have the same frequency. The wavelength change depends on the velocity change so that f is constant. If the velocity increases, the wavelength increases (direct relationship). Waves Changing Mediums Waves passing from one medium to another have the same frequency.

21 Superposition and Interference Principle of Superposition: Two or more waves occupying the same space. Interference: The result from two or more waves occupying the same space. Superposition and Interference Principle of Superposition: Two or more waves occupying the same space.

22 Constructive Interference Occurs when the wave displacements are in phase (crest meets crest or trough meets trough). The result is a wave with a larger amplitude than the individual waves. Constructive Interference Occurs when the wave displacements are in phase (crest meets crest or trough meets trough).

23 Destructive Interference Occurs when the wave displacements are out of phase (crest meets trough). The result is a wave with a smaller amplitude than the individual waves. Red: wave moving right Blue: wave moving left Green: superposition (Red + Blue wave) Destructive Interference Occurs when the wave displacements are out of phase (crest meets trough).

24 Destructive Interference If the pulses have unequal amplitudes, destructive interference is not complete. The pulse of the overlap is the algebraic sum of the two pulses. Red: wave moving right Blue: wave moving left Green: superposition (Red + Blue wave) Destructive Interference If the pulses have unequal amplitudes, destructive interference is not complete.

25 Standing Wave When the nodes and antinodes are stationary, the wave appears to be standing still. If you increase the frequency of a standing wave, you will see more nodes. Standing Wave When the nodes and antinodes are stationary, the wave appears to be standing still.

26 Superposition of Waves A. Two pulses traveling in opposite directions B. Two sine waves traveling in the same direction, but at different speeds C. Two sine waves traveling in opposite directions. http://paws.kettering.edu/~drussell/Demos/superposition/superposition.html Superposition of Waves A. Two pulses traveling in opposite directions B.

27 Nodes and Antinodes Node: The point in the medium that is completely undisturbed at all times. A node is produced by destructive interference of waves Antinode: The point of maximum displacement. An antinode is formed from constructive interference. Nodes and Antinodes Node: The point in the medium that is completely undisturbed at all times.

28 Harmonics Harmonics

29 Let’s check for understanding… The number of nodes in the standing wave shown in the diagram at the right is a.6 b.7 c.8 d.14 Let’s check for understanding… The number of nodes in the standing wave shown in the diagram at the right is a.6 b.7 c.8 d.14

30 Let’s check for understanding… The number of nodes in the standing wave shown in the diagram at the right is c.8 Let’s check for understanding… The number of nodes in the standing wave shown in the diagram at the right is c.8

31 Let’s check for understanding… The number of antinodes in the standing wave shown in the diagram at the right is a.6 b.7 c.8 d.14 Let’s check for understanding… The number of antinodes in the standing wave shown in the diagram at the right is a.6 b.7 c.8 d.14

32 Let’s check for understanding… The number of antinodes in the standing wave shown in the diagram at the right is b.7 Let’s check for understanding… The number of antinodes in the standing wave shown in the diagram at the right is b.7

33 Let’s check for understanding… In the standing wave shown, a. What is the amplitude? b. What is its wavelength? c. How many nodes are there? d. How many antinodes are there? Let’s check for understanding… In the standing wave shown, a.

34 Let’s check for understanding… In the standing wave shown, a. What is the amplitude? 10 cm b. What is its wavelength? c. How many nodes are there? d. How many antinodes are there? Let’s check for understanding… In the standing wave shown, a.

35 Let’s check for understanding… In the standing wave shown, a. What is the amplitude? 10 cm b. What is its wavelength? 1 m c. How many nodes are there? d. How many antinodes are there? Let’s check for understanding… In the standing wave shown, a.

36 Let’s check for understanding… In the standing wave shown, a. What is the amplitude? 10 cm b. What is its wavelength? 1 m c. How many nodes are there? 6 d. How many antinodes are there? Let’s check for understanding… In the standing wave shown, a.

37 Let’s check for understanding… In the standing wave shown, a. What is the amplitude? 10 cm b. What is its wavelength? 1 m c. How many nodes are there? 6 d. How many antinodes are there? 5 Let’s check for understanding… In the standing wave shown, a.

38 Reflection of Waves Normal: A line that is drawn perpendicular to the barrier (green). Angle of Incidence: The angle between the incidence ray and the normal. Angle of Reflection: The angle between the normal and the reflected ray. >I = >R Reflection of Waves Normal: A line that is drawn perpendicular to the barrier (green).

39 Refraction of Waves Refraction: The change in the direction of waves at the boundary between two different media. Refraction of Waves Refraction: The change in the direction of waves at the boundary between two different media.

40 Diffraction of Waves Diffraction: The spreading of waves around the edge of a barrier. Diffraction occurs when waves meet a small obstacle. They can bend around the obstacle, producing waves behind it. Diffraction of Waves Diffraction: The spreading of waves around the edge of a barrier.

41 Problem-Solving Problem-Solving

42 Springs Spring Constant Springs Spring Constant

43 Spring Constant (stiffness) A spring stretches 18 centimeters when a 56 Newton weight is suspended from it. What is the spring constant? Find: k Givens: d (x) = 18 cm = 0.18 m F = 56 N Formula: k = F d Solution: 310 N/m Spring Constant (stiffness) A spring stretches 18 centimeters when a 56 Newton weight is suspended from it.

44 Springs Potential Energy in a Spring Springs Potential Energy in a Spring

45 Period of a Pendulum Pendulum Period of a Pendulum Pendulum

46 Using a Pendulum A pendulum with a length of 36.9 centimeters has a period of 1.22 seconds. What is the acceleration due to gravity at the pendulum’s location? Find: a (g) Givens: d = 36.9 cm = 0.369 m T = 1.22 s Formula: g = 4  2 L T2T2 Solution: 9.78 m/s 2 Using a Pendulum A pendulum with a length of 36.9 centimeters has a period of 1.22 seconds.

47 Velocity, Wavelength, Frequency and Period Relationships Wavelength Velocity, Wavelength, Frequency and Period Relationships Wavelength

48 An 855 Hertz disturbance moves through an iron rail at a speed of 5130 meters per second. What is the wavelength of the disturbance? Find: Givens: f = 855 Hz v = 5130 m/s Formula: = v f Solution: 6.00 m An 855 Hertz disturbance moves through an iron rail at a speed of 5130 meters per second.

49 Velocity, Wavelength, Frequency and Period Relationships Period Velocity, Wavelength, Frequency and Period Relationships Period

50 An 855 Hertz disturbance moves through an iron rail at a speed of 5130 meters per second. What is the period of the disturbance? Find: T Givens: f = 855 Hz Formula: T = 1 f Solution: 0.00117 s An 855 Hertz disturbance moves through an iron rail at a speed of 5130 meters per second.

51 Velocity, Wavelength, Frequency and Period Relationships Velocity Velocity, Wavelength, Frequency and Period Relationships Velocity

52 A sound wave has a frequency of 192 Hertz and travels the length of a football field, 91.4 meters, in 0.271 seconds. What is the speed of the wave? Find: v Givens: f = 192 Hz d = 91.4 m t = 0.271 s Formula: v = d t Solution: 337 m/s A sound wave has a frequency of 192 Hertz and travels the length of a football field, 91.4 meters, in seconds.

53 Velocity A sonar signal of frequency 1.00 X 10 6 Hertz has a wavelength of 1.50 millimeters in water. What is the speed of the signal? Find: v Givens: f = 1.00 X 10 6 Hz = 1.50 mm = 0.00150 m Formula: v = f  Solution: 1.50 X 10 3 m/s Velocity A sonar signal of frequency 1.00 X 10 6 Hertz has a wavelength of 1.50 millimeters in water.


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