Lecture 27, Dec. 3WavesEnergy is transported in wave but the motion of matter is localTypes of WavesWave GraphsWave SpeedWave FormsContinuous Sinusoidal WaveWave Properties...Exercise Wave MotionWave PropertiesLook at the temporal (time-dependent) partExercise Wave MotionSlide 14Exercise Wave MotionSound, A special kind of longitudinal waveSoundSpeed of Sound Waves, GeneralWaves on a string...Slide 20Speed of Sound in a Solid RodWaves, Wave fronts, and RaysSlide 23Waves, Wavefronts, and RaysExercise Spherical WavesIntensity of soundsSlide 27Sound Level, ExampleLoudness and IntensityDoppler effect, moving sources/receiversDoppler effect, moving sources/receiversSlide 32Physics 207: Lecture 27, Pg 1Lecture 27, Dec. 3Goals:Goals:•Chapter 20Chapter 20 Employ the wave model Visualize wave motion Analyze functions of two variables Know the properties of sinusoidal waves, including wavelength, wave number, phase, and frequency. Work with a few important characteristics of sound waves. (e.g., Doppler effect)•AssignmentAssignment HW11, Due Friday, Dec. 5th HW12, Due Friday, Dec. 12th For Monday, Read through all of Chapter 21Physics 207: Lecture 27, Pg 2WavesA traveling wave is an organized disturbance propagating at a well-defined wave speed v.In transverse waves the particles of the medium move perpendicular to the direction of wave propagation.In longitudinal waves the particles of the medium move parallel to the direction of wave propagation.A wave transfers energy, but no material or substance is transferred outward from the source.Physics 207: Lecture 27, Pg 3Energy is transported in wave but the motion of matter is localPhysics 207: Lecture 27, Pg 4Types of WavesMechanical waves travel through a material medium such as water or air.Electromagnetic waves require no material medium and can travel through vacuum.Matter waves describe the wave-like characteristics of atomic-level particles.For mechanical waves, the speed of the wave is a property of the medium. Speed does not depend on the size or shape of the wave.Examples: Sound waves (air moves locally back & forth) Stadium waves (people move up & down) Water waves (water moves up & down) Light waves (an oscillating electromagnetic field)Physics 207: Lecture 27, Pg 5Wave GraphsThe displacement D of a wave is a function of both position (where) and time (when).A snapshot graph shows the wave’s displacement as a function of position at a single instant of time.A history graph shows the wave’s displacement as a function of time at a single point in space.The displacement, D, is a function of two variables, x and t, or D(x,t)Physics 207: Lecture 27, Pg 6Wave SpeedSpeed of a transverse, mechanical wave on a string: where Ts is the string tension and is linear string densitySpeed of sound (longitudinal mechanical wave) in air at 20°Cv = 343 m / sSpeed of light (transverse, EM wave) in vacuum: c = 3x108 m/sSpeed of light (transverse, EM wave) in a medium: v = c / nwhere n = index of refraction of the medium (typically 1 to 4)property inertialproperty elasticv sTvLmPhysics 207: Lecture 27, Pg 7Wave FormsSo far we have examined “continuous wavescontinuous waves” that go on forever in each direction !v v We can also have “pulses” caused by a brief disturbanceof the medium:v And “pulse trains” which aresomewhere in between.Physics 207: Lecture 27, Pg 8Continuous Sinusoidal WaveWavelengthWavelength: The distance between identical points on the wave.Amplitude: The maximum displacement A of a point on the wave.AAnimationPhysics 207: Lecture 27, Pg 9Wave Properties...Period: The time T for a point on the wave to undergo one complete oscillation.Speed: The wave moves one wavelength in one period T so its speed is v = / T.TvAnimationPhysics 207: Lecture 27, Pg 10Exercise Wave MotionThe speed of sound in air is a bit over 300 m/s, and the speed of light in air is about 300,000,000 m/s. Suppose we make a sound wave and a light wave that both have a wavelength of 3 meters. What is the ratio of the frequency of the light wave to that of the sound wave ? (Recall v = / T = f )(A) About 1,000,000(B) About 0.000,001(C) About 1000Physics 207: Lecture 27, Pg 11Wave PropertiesLook at the spatial part (Let t =0).Animation])//(2cos[(),(0 TtxAtxD)] )/2cos[()0,( xAxDWavelengthAyx•x = 0 y = A•x = /4 y = A cos(/2) = 0•x = /2 y = A cos() = -A]cos[),(0 tkxAtxDA = amplitude k = 2/ = wave number= 2f = angular frequency 0= phase constantPhysics 207: Lecture 27, Pg 12Look at the temporal (time-dependent) partLet x = 0)] )/2cos[(),( txAtxDPeriodAyt] )/2(cos[)cos(),0( tTAtAtD•t = 0 y = A•t =T / 4 y = A cos(-/2) = 0•t =T / 2 y = A cos(-) = -APhysics 207: Lecture 27, Pg 13Exercise Wave MotionA harmonic wave moving in the positive x direction can be described by the equation (The wave varies in space and time.) v = / T = f = ( ) ( f) = / k and, by definition, > 0D(x,t) = A cos ( (2 /) x - t ) = A cos (k x – t )Which of the following equation describes a harmonic wave moving in the negative x direction ?(A) D(x,t) = A sin (k x t )(B) D(x,t) = A cos ( k x t )(C) D(x,t) = A cos ( k x t )Physics 207: Lecture 27, Pg 14Exercise Wave MotionA boat is moored in a fixed location, and waves make it move up and down. If the spacing between wave crests is 20 meters and the speed of the waves is 5 m/s, how long t does it take the boat to go from the top of a crest to the bottom of a trough ? (Recall v = / T = f )(A) 2 sec (B) 4 sec (C) 8 sectt + tPhysics 207: Lecture 27, Pg 15Exercise Wave MotionA boat is moored in a fixed location, and waves make it move up and down. If the spacing between wave crests is 20 meters and the speed of the waves is 5 m/s, how long t does it take the boat to go from the top of a crest to the bottom of a trough ? T = 4 sec but crest to trough is half a wavelength(A) 2 sec (B) 4 sec (C) 8 sectt + tPhysics 207: Lecture 27, Pg 16Sound, A special kind of longitudinal waveConsider a vibrating guitar stringString VibratesPiece of string undergoes harmonic motionAir molecules
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