Transcript wave
Journal #20 3/9/12 What type of waves are represented in the diagram below? A B What is the main difference between these two types of waves? Chapter 14 – Waves and Chapter 15 - Sound Test will be on Friday, March 23 Vocab Quiz on 3-16-12 Quiz on 3-21-12 Periodic Motion Motions that repeat in a regular cycle are called periodic motions. Examples The include: blades of a fan moving in a circle The swinging of a pendulum The vibrations of a guitar string Simple Harmonic Motion (SHM) In simple harmonic motion, an object is pulled out of its equilibrium position and the resulting force on the object is directly proportional to the displacement of the object. At equilibrium Force required to return to equilibrium increases with displacement Vocabulary Check The amplitude is the MAXIMUM displacement from the equilibrium point. Greater amplitude means that there is a greater intensity or energy in the cycle. The period is the time it takes for one complete cycle. The symbol for period is T and is measured in seconds. The frequency is the number of cycles completed in one second. The symbol for frequency is f . Frequency is measured in units of hertz (Hz), named for Heinrich Rudolf Hertz(1857–94), a German physicist. Waves A wave is a rhythmic disturbance that carries energy through matter or space. The particles themselves only vibrate, they do not travel with the wave. There are 3 types of waves: Transverse Wave – a wave that vibrates perpendicular to the direction of wave motion. Longitudinal Wave – a wave that vibrates parallel to the direction of wave motion. Surface Waves – have the characteristics of both transverse and longitudinal waves. TRANSVERSE WAVES Motion of the particles is perpendicular to wave direction (energy). Examples include: string movements on musical instruments electromagnetic waves e.g. Light waves, x-rays, radio waves LONGITUDINAL WAVES Motion of particles is parallel to wave direction (energy). Sound travels as a longitudinal wave (also called a compressional wave because the particles of matter are compressed as the wave travels). SURFACE WAVES The particles in a surface wave travel in directions both perpendicular and parallel to the wave direction (energy). Picture of a Transverse Wave Crest l Wavelength A = Amplitude A Rest Position Trough Crest and Trough Crest – the peak, or highest point, of a wave Trough (pronounced “troff”) – the lowest point of a wave The height of the crest or trough is the amplitude of the wave. Wavelength (l) A wavelength is the shortest distance between points where the wave pattern repeats itself. The symbol is the Greek alphabet “Lamda” – l. The SI unit for wavelength in meters. One wavelength can be considered as one cycle of the wave. Period and Frequency Revisited The time it takes one cycle to pass a point is the period of the wave. seconds per cycle seconds cycle The number of wavelengths that pass a point per second is the frequency of the wave. cycles per second cycles second In symbolic form 1 T f or 1 f T Period and Frequency Practice What is the frequency of the second hand of a clock? Period = 60 sec Frequency = 1cycle/60 sec What is the frequency of US Presidential elections? Period = 4 yrs Frequency = 1 election/4 yrs What is the period of AC electricity in the US? Frequency = 60 Hz Period = 1 sec/ 60 cycles Calculating Speed of a Wave d l v f l t T Each of these combinations will result in a distance unit per time unit (m/s usually). Depending on the wording of the question, you can set any of these parts equal to each other to help you solve the question. Calculating Speed of a Wave Example Pepe and Alfredo are resting on an offshore raft after a swim. They estimate that 3.0 m separates a trough and an adjacent crest of each surface wave on the lake. They count 12 crests that pass by the raft in 20.0 s. Calculate how fast the waves are moving. d l v f l t T Two Important Wave Rules!! Speed is dictated by the medium (the type of matter). Frequency is dictated by the source (the object creating the vibration). Homework Textbook p.398 #75, 76, 78, 80, 81 Journal #21 3/14/12 What factor had the biggest effect on the period of a pendulum? Can you explain why the others had almost no effect at all? Journal #21 3/14/12 What factor had the biggest effect on the period of a pendulum? The length of the string has the greatest effect on the period of the pendulum. The longer the string, the longer the period. Can you explain why the others had almost no effect at all? Because gravity pulls on all objects equally, mass nor angle have a great effect on the period of a pendulum. Homework Answers p. 398 75. 76. 78. 80. 81. 8.3s 4.0 m/s a. 0.29 m/s; b. 0.21 s a. 550 Hz; b. 280; c. 170 m 1350 m Superposition of Waves Using the principle of superposition, two or more waves can be combined into a new wave. The result of the superposition is called interference. Constructive: when the crest of one wave overlaps the crest of another; “in phase”. Destructive: when the crest of one wave overlaps the trough of another; “out of phase”. Constructive Interference 2 waves in perfect phase Same frequency, greater amplitude Destructive Interference 2 waves perfectly out of phase Complete cancelation, Zero amplitude Standing Waves V Incident Wave V Reflected Wave Notice that the reflected wave is inverted Standing Wave V V Standing Waves When two sets of waves of equal amplitude and wavelength pass through each other in opposite directions, it is possible to create an interference pattern that looks like a wave that is “standing still.” The nodes of a standing wave never move, and the antinodes of a standing wave oscillate up and down. Draw the Following Diagram l There is no displacement at a node. There is maximum displacement at an antinode. Journal #22 3/15/12 Determine the number of wavelengths in the following examples. (hint: some of the examples will show divisions of ½ of a wave) Sound Sound travels as a longitudinal wave. Sounds audible to humans range from 20 - 20,000 Hz. As frequency increases, pitch rises. Loudness of Sound The amplitude of a sound wave is observed as loudness. Loudness is measured in decibels (dB). Most humans feel pain at about 125 decibels. Prolonged exposure to sounds of this loudness can cause permanent damage to the auditory sensory cells. Speed of Sound Pitch refers to how frequency is observed not speed. The speed of sound depends on medium and temperature. The speed of sound in air @ 0 ̊C is 331 m/s. It increases slightly with an increase in temperature. At room temp, sound travels at 340 m/s. Doppler Shift The apparent shift in frequency due to the motion of the object emitting the vibration OR the motion of the person perceiving the sound is called Doppler Shift. If the sound and the observer are approaching each other, there is an apparent increase in frequency. The opposite is true as well. Higher Pitch Honk! Lower Pitch How Sound Travels The blue dot to the right represents a speaker. The speaker is turned on. The first sound wave leaves the speaker. No sound is heard yet by the person. New sound waves emitted and expand outward. The person hears the sound when the sound waves reaches his ears. Doppler Shift Waves closer together results in higher pitch Waves farther apart results in lower pitch Super-sonic Speeds Traveling at the speed of sound is called mach 1 (pronounced “mock” 1) A sonic boom is the loud sound resulting from the incidence of a shock wave while crossing the “sound barrier”. A cone-shaped wave is made by an object moving at supersonic speed through a fluid. Sonic Boom Videos How a Shock Wave Forms x x x x x x x Pile-up of waves Shock Wave Journal #22 3/15/12 Complete the following waves with the required number of wavelengths: λ = 3½ λ = 2¾ λ = 4½ Frequency and Resonance The natural frequency of an object is the frequency it vibrates on its own Resonance is a condition that exists when the frequency of an applied force is the same as the natural frequency of vibration of an object or system Tacoma Narrows Bridge Video Fundamentals and Harmonics A fundamental of a string (or object) is the frequency that matches that objects natural frequency. Frequencies that occur at multiples of the fundamental are called harmonics. Harmonics of a String Each end of the string must end in a node!! Crystal Goblets Video Consonance and Dissonance Both of these terms are culturally dependent. Some cultures do not agree with each other on the pleasantness of certain chords (two or more pitches played at the same time). Consonance is when a chord has a pleasing sound. (Such as a C and an E on a keyboard… called a “major third”) Dissonance is when a chord has a displeasing sound. Beats When two notes of similar frequency are played at the same time, the combination of constructive and destructive interference creates audible pattern of loudness and softness. The closer the two notes are in frequency, the slower the beat.