2: Making the connection between mechanical waves on a string and Electromagnetic Waves. HELP due tonight

https://phet.colorado.edu/sims/html/wave-on-a-string/latest/wave-on-a-string_en.html

Reopen your mnmulation and reset the parameters you used in Part I of the lab. htt sat" het.colorado.eduisimsr'html'wave-ona-strin ilatestfwave-ona-strin en.html E 5 www.mm m 00:00:30 A II 2J ~ '5 J Is: A 0 Jo l'use Mn 1 11. Li 1' \"egg h \"MP" Imam E\"- Part 1: Interference and superposition of waves the effect of fixed and loose ended strings (4 pts) \\Ve will explore what happens to a wave pulse at the boundaryr when we have a loose end and a xed end. Restart the simulation. select Pulse mode and set: A = 1.0 cm. Damping = None. Tension = High. Pulse Width = 0.50s. 1. Send a single pulse and observe what happens to the pulse at the loose end. When a traveling wave or wave pulse encounters a boundary. some part of the wave bounces back (reection; and some part may continue to pass through the boundaly {Honsmission}. Describe the reected wave pulse in terms of the original pulse. Did the emptimde or the orientation change? (Did the pulse stay on the same side of the string or was it inverted or ipped over?) {1 pt) The pulse with a loose end turned into a reected pulse with no change in the amplitude. The orientation did change= the string ipped downward. 2. Restart and select xed end and observe what happens to the pulse when it is reected at the fixed end. How do the amplitude and orientation of the reected wave compare to reection from the loose end? Describe the difference between the two scenarios. (1 pt} The pulse with a xed end turned into a transmission wave with the amplitude remaining the same and the orientation changing where the string is ipped. The difference between the two is the interference. The rst interference was constructive interference and the second one was deconstructive interference with a point at the end on the light of the string a total deconstmctive interference. 3. Restart the simulation again with loose end. send a single pulse then send a second pulse just as the first pulse reaches the far end. Observe what happens when the two pulses overlap. The overlapping of two waves or wave pulses is called interference. The amplitude should be mice the original amplitudes. When waves overlap. the resulting amplitude is the sum of the two amplitudes. This is an example of the principle of superposition. "When the maxima of both waves are at the same location on the string at the same time. we call this constructive interference. Pause the simulation just before the two pulses overlap. then step it forward to when the amplitude reaches its maximum v alue. Measure the amplitude and record your answ e1 here: _.1 9cm (1 pt} The interference is chum-Le 4. Hit Play again and let the pulses reect and pause just before they meet. In this case. the two pulses should have opposite amplitudes {one positive. one negative}. Step through the simulation as the two pulses overlap. 'What is the amplitude when they are fully overlapped? 4cm This is called destructive interference. (1 pt) 2: lilaking the connection between mechanical waves on a string and Electromagnetic 'Waves. (6 pts) For any mechanical wave the wavefimction contains all the information about the propagation speed and direction of the wave. The wave speed is set by the medium. which was represented by the tension in the string. Chapters 14. 15. and 16 in your text develops of the wavefunction starting with the simple harmonic motion (Ch 14} of a mass oscillating on a spring about its equilibrium position. The mathematics also applies to a pendulum swinging back and forth and many other phenomena. The equation only had a time variable. t. and was described equally well by either a sine or a cosine function. For the mass on the spring. we generally applied a force to displace the mass by stretching the spring then let it go. Because we started at the maximum displacement at time t = D. we chose the cosine function to describe the motion: x(t) = Acoswt) = Aces (gt) = Acos2nft) They also discussed the velocity and acceleration of the object that was oscillating and showed that they were also sinusoidal functions and showed the similarities both graphically and mathematically. taking successive slopes of the graph. or time derivatives of the function. led to 1910) = wAsin{wt); and 1118) = w2Acos(wt) Chapter 15 introduced the wave model. which included transverse and longitudinal waves. with the addition of the spatial variable (x. y. or 2) added to the inside of the sinusoidal function. Traveling waves all have 2 distinct motions 1} the back-"forth. tip-"down. or side to side oscillation of the medium. which is described by the oscillatory sine or cosine functions and their derivatives. and 2} the propagation of the wave carrying energy through the medium. In all these cases the medium determines the propagation speed, v. with a similar form: restoring force returning system to equilibrium ' ' ' ' ' _) 1? _ T_ I? _ l'kBT _ YR? Enerttaresistingreturn toequiiibri'um string _ 11' sound _ m _ M For waves on a string. T is the tension (in newtons. N) and pi is the mass per unit length of the string (in kgi'm). both \"medium For waves on a string. T is the tension (in newtons. N) and la is the mass per unit length of the string {in kg.-"m). both physical properties of the string. For sound waves in a gas. I is the absolute temperature of the gas (in kelvin}. R is the ideal gas constant. M is the molar mass. and the parameter )3 is a constant that depends on whether the gas is monoatomic. diatomic. or other. Again. these all describe the physical properties of the medium. Sound also travels though liquids and solids. and when it does there is a similar ratio with parameters that describe the bulk properties (density. elasticity. etc.) of the medium. In all cases. the waves could be described by the same wave function: y(x, t) = Acoscx out) or yr, t) = Asincx not). The wave speedT and the propagation direction are "hidden\" in the coeicients in front of the spatial (x) and temporal (I) variables. Of course. all waves are not limited to propagating along the x-axis and having their amplitudes along the y-axis. but we can extract that information from the wavefunction itself. no matter what order the space and time variables are written or whether the function is a sine or cosine. the spatial direction is always the spatial variable 2H inside the sinusoidal function (x. y. or 2) and its coeicient is always k = T and the coefcient in 'ont of the time variable (I) is always to = Zirf = 2113. Hence. from the wavefunction we can extract the wave speed v. the propagation axis through space. and we can tell if the wave is propagating in the positive. +. or negative. . x. y. or 2'. directions by the relative signs in 'ont of each teim. If both signs are the same. the wave propagates in the negative direction. if the two terms have different signs. it does not matter which. the wave propagates in the positive direction. This is true for any mechanical wave in any medium. Given the following wave function. determine the ampiimdeA. wavemimber it. wavelength .1. eqaeney angular 'equeney a). period T. and propagation direction of the wave (as =|= x. y. or z}. (6 pts) my = {3.75 In} cos[[42.5 rad/\"ink + (98.6 radish]