Standing Waves, Natural Frequency, & Resonance. Physics 5 th /6 th 6wks

Transcription

1 Standing Waves, Natural Frequency, & Resonance Physics 5 th /6 th 6wks

2 Wave Relationships & Related Terms Frequency, Wavelength, and Energy: Frequency, like the amplitude, is an indicator of wave strength and wave energy. The greater it is the greater the energy of a wave. There is a direct relationship between energy and frequency, just as there is between amplitude and energy. As the frequency gets higher, the wavelength gets smaller and vice versa Therefore, waves with higher energy tend to have high frequency and low wavelengths and those with lower energy tend to have low frequency and larger wavelengths. There is an indirect relationship between frequency and wavelength There is an indirect relationship between energy and wavelength

3 Wave Damping Damping the decrease in the amplitude of a wave over time. Damping is the result of friction reducing the energy of a wave. Note: as damping occurs, frequency and wavelength remain the same if no other energy is added

4 An Appetizer

5 Yet another appetizer

6 Standing Waves an Introduction

7 Standing Waves Standing wave a special type of wave pattern that forms when transverse waves equal in wavelength and amplitude, but traveling in opposite directions, continuously interfere with each other Standing waves are produced when two waves of equal amplitude and wavelength pass through each other in opposite directions (usually formed when the incident wave the original wave, and the reflected wave interfere with each other The waves create a pattern of crests and troughs that do not seem to be moving, and because the wave pattern stays in one place, it is called a standing wave.

8 Standing waves and harmonics

9 Standing Waves antinodes Interference occurs as the waves coming from each end overlap. Where either two crests or two troughs meet they combine to form a new wave with a greater amplitude. The places where waves add to each other are called antinodes. At these places, the vibrating item experiences the greatest amplitude. Note: as there are more and more antinodes (that is as the number of the harmonic - which is the number of antinodes increases) the amplitude of the vibrating object gets smaller and smaller. For a vibrating item, exhibiting standing waves, amplitude and frequency are inversely related.

10 Standing Waves nodes Nodes the places where the two waves always cancel each other out. These are places were the media the wave is traveling through do not move. But where crests and troughs meet, the waves cancel each other out. The easiest standing wave to produce is at the natural frequency of the media the wave is traveling through. The natural frequency (aka the first harmonic, the fundamental, and the resonant frequency) experiences the largest vibration at the least amount of energy.

11 Wave Reflection and Standing Waves in a Spring

12 Nodes and Antinodes Node Antinode Node Antinode Node

13 Standing waves A traveling wave represents a disturbance that moves from one location to another location at a speed which depends on the elastic and inertia properties of the medium. The animation at left shows two traveling waves: the blue wave is traveling to the right and the red wave is traveling to the left. Both waves have the same amplitude, the same frequency, and the same wavelength. The black signal in the animation represents the superposition of these two oppositely directed traveling waves. As these waves pass through each other and add together, they create a standing wave - a pattern which neither moves left or right, but simply oscillates up and down as a function of time. The amplitude of this standing wave is twice that of the individual waves when the two waves are in phase so that peaks and valleys line up. The amplitude of the standing wave is zero when the two waves are completely opposite phase so that they peaks of one wave line up with the valleys of the other wave; the two wave amplitudes cancel each other out.

14 Standing Waves due to two reflecting waves overlapping

15 Standing waves continued All objects have a certain frequency or set of frequencies that vibrations pass through them. That frequency (or set of frequencies) is based upon a) the nature of the material (density, tension, temperature, etc.) and b) the size of the material (usually the length such as the length of a string waves pass through). Changing the size/length/nature of a medium changes frequency Multiples of the natural frequency are called harmonics. The natural frequency of an object is also known as the first harmonic, the fundamental, and the resonant frequency When you pump a swing in rhythm with the natural frequency of the swing you produce larger and larger amplitudes, making it go higher and higher. If energy is absorbed, the object can vibrate so strongly that its amplitude will steadily increase, possibly breaking it apart if the material is brittle.

16 Standing waves and a guitar

17 Standing waves continued If the natural frequency of the string was 20 Hz Then the 5 th harmonic would occur at 5 x 20 Hz = 100 Hz Note: at the fundamental or 1 st harmonic, a standing wave has 2 nodes & 1 antinode Note: at the 5 th harmonic, a standing wave has 6 nodes and 5 antinodes Did you catch the trend? There is one more node than antinodes, & the number of antinodes = the harmonic

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19 Note: 2 antinodes = 1 wavelength since

20 The Natural Frequency and Harmonics of a Vibrating Object 1 st Harmonic Frequency = 1 x Natural Frequency λ= λ = length of material (0.5 x harmonic) 1 (0.5 x 1) = 2 units 2 nd Harmonic Frequency = 2 x Natural Frequency λ= λ = length of material (0.5 x harmonic) 1 (0.5 x 2) = 1 unit 3 rd Harmonic Frequency = 3 x Natural Frequency λ= λ = length of material (0.5 x harmonic) 1 (0.5 x 3) 0.7 units

21 Finding the number of wavelengths To find the number of wavelengths that are present, all you need to do is count the number of antinodes that you see, since every two antinodes is one wavelength. Example: Number of Antinodes Number of λ= 2 Number of λ = 6 Antinodes = 3 λ 2

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23 Finding the Frequency of a Standing Wave F H N F f

24 Finding the Speed of a Standing Wave

25 Standing Waves antinode 1 st harmonic 2 nd harmonic 3 rd harmonic

26 Natural Frequency and Resonance Galloping Gertie When any object composed of an elastic material is disturbed, it vibrates at its own special set of frequencies. An object s natural frequency depends upon its elasticity and its shape. Most things from planets to atoms and almost everything else in between have a springiness to them and vibrate at one or more natural frequencies A natural frequency is one at which minimum energy is required to produce forced vibrations Applying energy to an object at its natural frequency produces larger amplitudes.

27 Standing waves on bridge in Volgograd, Russia

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29 Natural Frequency and Resonance In an English context, to resonate means to agree with harmoniously as in Gen. Smith s speech on national defense resonated with the audience of graduating army cadets. Resonance the ability of an object to vibrate by absorbing energy at its natural frequency. Resonance is also the ability of objects to oscillate at a higher amplitude at some frequencies than at others. An object will resonate, or vibrate at its natural frequency or at one of its harmonics - whenever something delivers energy to it at that frequency. A singer like Jamie Vendera is able to use resonance to break a glass when he sings at the resonant frequency (the fundamental) of the glass at a high enough volume (amplitude) so that the brittle glass shakes apart. Dr Hewitt Resonance Demo

30 Dr. Hewitt and Resonance

31 Resonance: Forced vs. Sympathetic Vibration If you physically come in direct contact with an item and cause it to vibrate it will vibrate at its natural frequency. This is a forced vibration. Resonance is when one object, vibrating at the natural frequency of a second object, forces that 2 nd object into vibrational motion. Since resonance is accomplished through a third party or proxy (like a singer s vocal chords sending energy through air particles at the natural or resonant frequency to a glass) we call the vibrations cause by resonance sympathetic vibrations

32 Resonance of Inverted Pendulums

33 A Resonating Wine Glass in Slow Motion

34 Some fun things sound waves can do