Chapter 14 Waves http://faraday.physics.utoronto.ca/iyearlab/intros/standingwaves/flash/long_wave.html Apr 30 7:11 AM May 5 7:16 AM 1

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If you want to transfer energy to from one point to another what options do you have? rock B A Apr 21 11:12 AM 3 ways to tranfer energy from one place to another 1) direct contactpush or pull 2) use of projectiles 3) use waves Apr 24 7:21 AM 5

What is a Wave? Definition of a Wave Webster's dictionary defines a wave as "a disturbance or variation that transfers energy progressively from point to point in a medium and that may take the form of an elastic deformation or of a variation of pressure, electric or magnetic intensity, electric potential, or temperature." The most important part of this definition is that a wave is a disturbance or variation which travels through a medium. The medium through which the wave travels may experience some local oscillations as the wave passes, but the particles in the medium do not travel with the wave. The disturbance may take any of a number of shapes. Have you ever "done the wave" as part of a large crowd at a football or baseball game? A group of people jumps up and sits back down, some nearby people see them and they jump up, some people further away follow suit and pretty soon you have a wave travelling around the stadium. The wave is the disturbance (people jumping up and sitting back down), and it travels around the stadium. However, none of the individual people the stadium are carried around with the wave as it travels they all remain at their Apr 25 7:14 AM What is a Wave? A disturbance that carries energy through matter or space. what it is what it does how it does it caused by vibration Apr 29 3:24 PM 6

Types of Waves Mechanical requires a medium Electromagnetic requires no medium characteristics of medium determine speed of wave anything made of matter with IM bonds all EM waves travel at 3.0 x 10 8 m/s...slower in mediums Apr 30 8:01 AM Transverse waves on a string are another example. The string is displaced up and down as the wave travels from left to right, but the string itself does not experience any net motion. http://www.ngsir.netfirms.com/englishhtm/twavea.htm Apr 30 7:24 AM 7

Transverse Waves In a transverse wave the particle displacement is perpendicular to the direction of wave propagation. The animation below shows a onedimensional transverse plane wave propagating from left to right. The particles do not move along with the wave; they simply oscillate up and down about their individual equilibrium positions as the wave passes by. Pick a single particle and watch its motion. Oscillator vibrates (moves) up and down perpendicular to the direction the wave travels Apr 25 6:56 AM Longitudinal Waves In a longitudinal wave the particle displacement is parallel to the direction of wave propagation. The animation below shows a one dimensional longitudinal plane wave propagating down a tube. The particles do not move down the tube with the wave; they simply oscillate back and forth about their individual equilibrium positions. Pick a single particle and watch its motion. The wave is seen as the motion of the compressed region (ie, it is a pressure wave), which moves from left to right. Oscillator vibrates (moves) back and forth parallel to the direction the wave travels Apr 25 6:56 AM 8

Wave Chacteristics frequency/period (use stop watch) http://phet.colorado.edu/simulations/stringwave/stringwave.swf wave on a string_en.jar Apr 29 3:41 PM Longitudinal sound waves in air behave in much the same way. As the wave passes through, the particles in the air oscillate back and forth about their equilibrium positions but it is the disturbance which travels, not the individual particles in the medium. Apr 25 7:16 AM 9

Compression Rarefaction Wavelength (λ) http://www.ngsir.netfirms.com/englishhtm/lwave.htm May 1 6:47 AM v = fλ dependant on frequency and velocity determined by characteristics ofmedium determined by source rate it vibrates May 1 9:05 AM 10

+ Frequency determined by source f s = f w f s = 1/T T = 1/f "f " = waves/s "f" is in Hz: waves/s "T" = s/wave "T" = period: time for one wave Velocity determined by medium solids liquids/gases v= E/ρ v= β/ρ wire/string v= T /µ basic wave equation May 1 8:26 AM v= fλ Examples: Sound is produced by a vibrating tuning fork. a) If the tuning fork vibrates at 256 Hz, what is the wavelength of the sound? Sound travels at 340 m/s in air. b) What is the period of the wave? a) v= fλ λ = v/f λ = (340 m/s)/256 Hz = 1.33 m Hz = 1/s b) T = 1/f = 1/256 Hz =.0039 s λ = v/f λ = (m/s)/(1/s) λ = m http://4a4b.wikispaces.com/file/view/ear.jpg/49525655/ear.jpg Apr 27 9:13 AM 11

Examples: Lightening strikes and you see the flash and then hear the thunder 5.0 s later. a) What is the speed of sound if the strike occurred 1700 m away? b) What is the speed of light if it only took 5.67 x 10 6 s to travel the same distance? a) v s = d/t = 1700 m/5s = 340 m/s b) v l = d/t = 1700 m/5.67 x 10 6 s = 3.0 x 10 8 m/s c) If one mile is 1610 m, how long does it take sound to travel 1 mile? v s = d/t t = d/v s = 1610 m/340 m/s = 4.6 s http://en.wikipedia.org/wiki/lightning Apr 27 9:24 AM Water Waves (surface waves) Water waves are an example of waves that involve a combination of both longitudinal and transverse motions. As a wave travels through the water, the particles travel in clockwise circles. The radius of the circles decreases as the depth into the water increases. The simulation below 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. Identified below are two particles in blue to show that each particle indeed travels in a clockwise circle as the wave passes. Apr 25 6:56 AM 12

Rayleigh surface waves Another example of waves with both longitudinal and transverse motion may be found in solids as Rayleigh surface waves. The particles in a solid, through which a Rayleigh surface wave passes, move in elliptical paths, with the major axis of the ellipse perpendicular to the surface of the solid. As the depth into the solid increases the "width" of the elliptical path decreases. Rayleigh waves are different from water waves in one important way. In a water wave all particles travel in clockwise circles. However, in a Rayleigh surface wave, particles at the surface trace out a counterclockwise ellipse, while particles at a depth of more than 1/5th of a wavelength trace out clockwise ellispes. The movie below shows a Rayleigh wave travelling from left to right along the surface of a solid. I have identified two particles in blue to illustrate the counterclockwise clockwise motion as a function of depth. Apr 25 7:12 AM Apr 26 11:05 AM 13

Apr 26 11:08 AM Two waves with slightly different frequencies are travelling to the right. The resulting wave travels in the same direction and with the same speed as the two component waves. The "beat" wave oscillates with the average frequency, and its amplitude varies according to the difference frequency. f b = f 1 f 2 Apr 25 7:22 AM 14

Apr 28 10:56 AM The animation below shows a wave pulse travelling on a string. The speed, v, with which the wave pulse travels along the string depends on the elastic restoring force (tension, T) and inertia (mass per unit length, ) according to v = T/µ Apr 25 8:38 AM 15

A string is 90 cm long and has a frequency of 256 Hz. What is its wavelength? The medium (wire) holds 1/2 the wave, there the wave is twice the size of the medium 1.8 m. v= fλ v = 256 Hz (1.8 m) v= 461 m/s What is "µ" if the tension is 120 N? v = T/µ µ = T/v 2 = 120 N/(461 m/s) 2 =.00056kg /m 90 cm Apr 29 11:06 AM The exact location where one medium ends and another one starts when wave travels: when wave travels: May 1 8:36 AM 16

Whenever a wave passes from one medium to another it is partially transmitted and partially reflected continuim May 5 1:52 PM Reflection from a HARD (Rigid) boundary The animation at left shows a wave pulse on a string moving from left to right towards the end which is rigidly clamped. As the wave pulse approaches the fixed end, the internal restoring forces which allow the wave to propagate exert an upward force on the end of the string. But, since the end is clamped, it cannot move. According to Newton's third law, the wall must be exerting an equal downward force on the end of the string. This new force creates a wave pulse that propagates from right to left, with the same speed and amplitude as the incident wave, but with opposite polarity (upside down). Apr 25 7:23 AM 17

Reflection from a SOFT (Free) boundary The animation at left shows a wave pulse on a string moving from left to right towards the end which is free to move vertically (imagine the string tied to a massless ring which slides frictionlessly up and down a vertical pole). The net vertical force at the free end must be zero. This boundary condition is mathematically equivalent to requiring that the slope of the string displacement be zero at the free end (look closely at the movie to verify that this is true). The reflected wave pulse propagates from right to left, with the same speed and amplitude as the incident wave, and with the same polarity (rightside up). => at a free (soft) boundary, the restoring force is zero and the reflected wave has the same polarity (no phase change) as the incident wave Apr 25 7:23 AM From low speed to high speed (high density to low density) slower to faster Free Termination In this animation the incident wave is travelling from a high density (low wave speed) region towards a low density (high wave speed) region. => How do the amplitudes of the reflected and transmitted waves compare to the amplitude of the incident wave? => How do the polarities of the reflected and transmitted waves compare to the polarity of the incident wave? => How do the widths of the reflected and transmitted waves compare to the width of the incident wave? Apr 25 7:23 AM 18

Velocity solids liquids/gases wire/string basic wave equation v= E/ρ v= β/ρ v= T /µ v= fλ "E" = elastic modulus for solids (tell elastic properties of solidmeasure of strength of intermolecular bonds "β" = bulk modulus for liquids and gases (tells elastic properties of liquids.gases measure of strength of intermolecular bonds v= d/t Apr 30 7:17 AM (low density to high density) Termination... faster to slower Rigid In this animation the incident wave is travelling from a low density (high wave speed) region towards a high density (low wave speed) region. => How do the amplitudes of the reflected and transmitted waves compare to the amplitude of the incident wave? => How do the polarities of the reflected and transmitted waves compare to the polarity of the incident wave? => How do the widths of the reflected and transmitted waves compare to the width of the incident wave? Apr 25 7:23 AM 19

Superposition The movie below shows two gaussian wave pulses travelling on a string, one is moving to the right, the other is moving to the left. They pass through each other without being disturbed, and the net displacement is the sum of the two individual displacements. It should also be mentioned that this string is nondispersive (all frequencies travel at the same speed) since the Gaussian wave pulses do not change their shape as they propagate. If the medium was dispersive, then the waves would change their shape. Apr 25 7:20 AM Apr 28 11:10 AM 20

The movie below shows how a standing wave may be created from two travelling waves. If two sinusoidal waves having the same frequency (wavelength) and the same amplitude are travelling in opposite directions in the same medium then, using superposition, the net displacement of the medium is the sum of the two waves. As the movie shows, when the two waves are 180 out of phase with each other they cancel, and when they are in phase with each other they add together. As the two waves pass through each other, the net result alternates between zero and some maximum amplitude. However, this pattern simply oscillates; it does not travel to the right or the left. I have placed two dots on the string, one at an antinode and one at a node. Which is which? Apr 25 7:21 AM The animation below shows two sinusoidal waves travelling in the same direction. The phase difference between the two waves varies increases with time so that the effects of both constructive and destructive interference may be seen. First of all, notice that the sum wave (in blue) is a travelling wave which moves from left to right. When the two gray waves are in phase the result is large amplitude. When the two gray waves become out of phase the sum wave is zero. Apr 25 7:20 AM 21

Standing waves: http://www.ngsir.netfirms.com/englishhtm/twavestata.htm http://www.walter fendt.de/ph14e/stwaverefl.htm incident/reflected/standing wave May 1 6:52 AM Doppler Effect car horn http://www.upscale.utoronto.ca/generalinterest/harrison/flash/classmechanics/dop plerwavefronts/dopplerwavefronts.html stationary source vel source < vel wave vel source = vel wave vel source > vel wave Apr 24 7:08 AM 22

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Attachments wave on a string_en.jar