Slide 1 / 37 Slide 2 / 37 Algebra Based Physics Waves 2015-12-01 www.njctl.org Slide 3 / 37 Slide 4 / 37 Table of Contents Click on the topic to go to that section Wave Motion · Types of Waves · Wave Motion Interference · Standing Waves on a String · Return to Table of Contents https://www.njctl.org/video/?v=YWGToS4Xmqo Slide 5 / 37 Slide 6 / 37 Wave Motion Wave Motion All types of traveling waves transport energy. Study of a single wave pulse shows that it is begun with a vibration and transmitted through internal forces in the medium. Continuous waves start with A wave travels along its vibrations too. If the vibration medium, but the is SHM, then the wave will be individual particles just sinusoidal. move up and down.
Slide 7 / 37 Slide 8 / 37 Wave Motion Wave Motion Wave characteristics: Wave velocity is the velocity at which wave crests (or any · Amplitude, A other part of the wave) moves. · Wavelength, · Frequency f and period T A wave crest travels a distance of one wavelength, , in one period, T. · Wave velocity Wave velocity is: Slide 9 / 37 Slide 10 / 37 What is the wave speed if the period of a wave is 4 seconds A fisherman noticed that a float makes 30 oscillations in 15 1 2 and the wavelength is 1.8 m? seconds. The distance between to consecutive crests is 2 m. What is the wave speed? https://www.njctl.org/video/?v=l71SqE_nQ3o https://www.njctl.org/video/?v=833UXXiacJ0 Slide 11 / 37 Slide 12 / 37 Wave Motion What is the wavelength of a wave traveling with a speed of 3 6 m/s and a period of 3s? The velocity of a wave depends on the medium through which it is traveling. The velocity of a wave on a stretch string is related to the tension force in the string and the mass per unit length of the string. Where F T is the tension in the string and is the mass per unit length (m/L). https://www.njctl.org/video/?v=A5k1j919Fd8 https://www.njctl.org/video/?v=dwahaT-JVGk
Slide 13 / 37 Slide 14 / 37 4 What happens to the speed of a wave on a string if the tension of 5 What happens to the speed of a wave on a string if the mass the string is increased by a factor of nine? per unit length of the string is increased by a factor of nine? A It is decreased by a factor of 3. A It is decreased by a factor of 3. B It is decreased by a factor of 9. B It is decreased by a factor of 9. C It is increased by a factor of 3. C It is increased by a factor of 3. D It is increased by a factor of 9. D It is increased by a factor of 9. https://www.njctl.org/video/?v=JBzhgL0ZvF8 https://www.njctl.org/video/?v=Qv1PZt-Z0ZM Slide 15 / 37 Slide 16 / 37 Types of Waves: Transverse and Longitudinal Types of Waves The motion of particles in a wave can either be perpendicular to the wave direction (transverse) or parallel to it (longitudinal). Return to Table of Contents https://www.njctl.org/video/?v=CwFotYt7sYo Slide 17 / 37 Slide 18 / 37 Types of Waves: Transverse and Longitudinal Sound waves are longitudinal waves: Interference Return to Table of Contents https://www.njctl.org/video/?v=dLz6j50fqxk
Slide 19 / 37 Slide 20 / 37 Reflection and Transmission of Waves Reflection and Transmission of Waves A wave reaching the end of its medium, but where the medium is still free to move, will be reflected (b), and its reflection will be upright. A wave encountering a denser medium will be partly A wave hitting an obstacle will be reflected (a), and reflected and partly transmitted; if the wave speed is less in its reflection will be inverted. the denser medium, the wavelength will be shorter. Slide 21 / 37 Slide 22 / 37 Interference; Principle of Superposition Reflection and Transmission of Waves The superposition principle says that when two waves pass through the same point, the displacement is the arithmetic sum of the individual displacements. In the figure below, (a) exhibits destructive interference and (b) exhibits constructive interference. A wave encountering a lighter medium will be partly reflected and partly transmitted; if the wave speed is greater in the denser medium, the wavelength will be longer. Slide 23 / 37 Slide 24 / 37 Reflection and Transmission of Waves Interference; Principle of Superposition Two- or three-dimensional waves can be represented by These figures show the sum of two waves. In (a) they add wave fronts, which are curves of surfaces where all the constructively; in (b) they add destructively ; and in (c) they add waves have the same phase. partially destructively . Lines perpendicular to the wave fronts are called rays; they point in the direction of propagation of the wave.
Slide 25 / 37 Slide 26 / 37 6 What is the result at an oscillating point if two waves reach this 7 What is the result at an oscillating point if two waves reach this point one half of a wavelength apart? point two full wavelengths apart? A Constructive interference A Constructive interference B Destructive interference B Destructive interference C Partially destructive interference C Partially destructive interference https://www.njctl.org/video/?v=tmRCRJg1PaQ https://www.njctl.org/video/?v=yoXJJGvCFvo Slide 27 / 37 Slide 28 / 37 8 What is the result at an oscillating point if two waves reach this point one quarter of a wavelength apart? A Constructive interference B Destructive interference C Partially destructive interference Standing Waves on a String Return to Table of Contents https://www.njctl.org/video/?v=DeALLoYU_e0 https://www.njctl.org/video/?v=JiYC5EJ754w Slide 29 / 37 Slide 30 / 37 Standing Waves; Resonance Standing Waves; Resonance Standing waves occur when both ends of a string are fixed. In that case, only The frequencies of the standing waves which are waves on a motionless at the ends of the particular string are called string can persist. resonant frequencies. There are nodes, where the They are also referred to as amplitude is always zero, the fundamental and harmonics. and antinodes, where the amplitude varies from zero to the maximum value.
Slide 31 / 37 Slide 32 / 37 Standing Waves; Resonance 9 What is the wavelength of the wave shown below? The wavelengths and frequencies of standing waves are: 5m https://www.njctl.org/video/?v=5AJbklN6mNY Slide 33 / 37 Slide 34 / 37 10 What is the wavelength of the wave shown below? 11 If the speed of the wave is 8m/s, what is the frequency of this wave? 10m 10m https://www.njctl.org/video/?v=dFpW68xyZBQ https://www.njctl.org/video/?v=dWS5e7wi6-s Slide 35 / 37 Slide 36 / 37 Summary Summary Vibrating objects are sources of waves, which may be Transverse wave: oscillations perpendicular to direction of wave either a pulse or continuous. motion. Wavelength: distance between successive crests . Longitudinal wave: oscillations parallel to direction of wave motion. Frequency: number of crests that pass a given point per unit time. Amplitude: maximum height of crest. Wave velocity: For a wave on a string:
Slide 37 / 37 Summary When two waves pass through the same region of space, they interfere. Interference may be either constructive or destructive. Standing waves can be produced on a string with both ends fixed. The waves that persist are at the resonant frequencies. Nodes occur where there is no motion; antinodes where the amplitude is maximum. Waves refract when entering a medium of different wave speed, and diffract around obstacles.
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