{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Transverse Waves" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Transverse waves are waves where the displacement of the medium (e.g. the string) is perpendicular (or transverse) to the direction of wave propagation. So, for instance, the string is displaced in the y\n", "direction while the wave travels in the x direction. " ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Driving a Wave" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Until now, we have not thought about how waves start and finish: we\n", "have assumed (implicitly) that they are infinite in time and space.\n", "However, this is not how real systems work: if a wave is to continue\n", "to propagate along a string (or down an optical fibre, say) then there\n", "must be some driving force. Let's consider a string stretched to a\n", "length $L$ with ends at $x=0$ and $x=L$. We'll place a driving\n", "mechanism of some kind at $x=0$. \n", "\n", "What must the driving mechanism do ? It needs to produce a force which\n", "balances the transverse component of the tension in the string at\n", "$x=0$. This is a driving force: \n", "\n", "\\begin{equation}\n", " F_D = -T\\left(\\frac{\\partial \\psi}{\\partial x}\\right)_{x=0} = \\frac{T}{c} \\left(\\frac{\\partial \\psi}{\\partial t}\\right)_{x=0} = Z_0 \\left(\\frac{\\partial \\psi}{\\partial t}\\right)_{x=0}\n", "\\end{equation}\n", "\n", "We have used the travelling wave equation from Chapter 3 to\n", "simplify. The force at any instant (or instantaneous force) must be\n", "proportional to the transverse velocity of the string---which closely\n", "resembles a standard drag force in a damped harmonic oscillator. Why\n", "do we have this drag ? It arises from the energy being transported by\n", "the wave: if we want to keep a constant wave motion going, we must put\n", "energy into the system. Notice that the constant of proportionality\n", "is the characteristic impedance. It is a function\n", "of the system only (in this case the tension and mass density) and\n", "does not depend on the type of motion or its frequency. " ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Terminating a wave" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have just seen that creating or driving a wave along a stretched\n", "string (or, in fact, in any medium) requires energy to be put in to\n", "the system. But what about the other end of the string ? What happens\n", "there ? Let's think about a _finite_ string, and how we can make\n", "it resemble an infinite string. We know what force we need at $x=0$\n", "to create the wave. At the end of the string, $x=L$, we need a\n", "transverse force to balance tension in the string; if we match this\n", "tension then it will be as if the end was not there. This condition\n", "can be written: \n", "\n", "\\begin{equation}\n", " F_L = T\\left(\\frac{\\partial \\psi}{\\partial x}\\right)_{x=L} = -Z_0 \\left(\\frac{\\partial \\psi}{\\partial t}\\right)_{x=L}\n", "\\end{equation}\n", "\n", "So if we have some form of drag to absorb the energy being transmitted\n", "along the string, then the wave will propagate along as if the string\n", "were infinite (assuming that we have set up the driver as described\n", "above). This idea is known as _impedance matching_ and is\n", "important in many areas, particularly electromagnetism (where we must\n", "terminate, say, a power line or an aerial correctly). Remember that\n", "this all came about because we have a _finite_ string (or medium\n", "in general) which we want to send a wave down, with the medium\n", "behaving _as if it were infinite_. This means that we must put\n", "energy in at one end, and take it out at the other. \n", "\n", "If we do _not_ provide the right force at the end, then something\n", "different will happen. In fact, these ideas can be extended to\n", "consider _boundaries_ between different media (e.g. tying a light\n", "string to a rope, or light going from air into water or glass). The\n", "two media will have different impedances (in the case of the string\n", "and rope, probably different mass densities even if they're under the\n", "same tension) and something interesting will happen at the boundary. " ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Reflection and Transmission" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Imagine a string under tension, with one end tied to a solid object\n", "(like a wall) and the other end free to be driven. If we send a pulse\n", "down the string (for example by moving the free end up and then down\n", "rapidly once), it will propagate along the string as a travelling\n", "wave. What will happen when it reaches the solid wall ? Intuition or\n", "experience tells us that when a wave reaches a solid object (i.e. an\n", "object with very large impedance) it tends to be reflected. A\n", "reflected wave in one dimension travels in the _opposite_\n", "direction to the incoming wave, so we will need _both_ solutions\n", "for the wave equation (i.e. $\\psi = \\psi_i + \\psi_r = f(x-ct) +\n", "g(x+ct)$, where $\\psi_i$ is the incoming or _incident_ wave and\n", "$\\psi_r$ is the reflected wave). We can also deduce this need for\n", "both waves from a more general situation we'll see below.\n", "\n", "Now, we need to work out the relationship between the two components\n", "of the wave, and we'll do this by thinking about the _boundary\n", " conditions_ on the wave. Much of the work done in physics involves\n", "working out appropriate boundary conditions, and solutions of\n", "differential equations given appropriate boundary conditions. We will\n", "assume that the solid wall has an infinite impedance, so there can be\n", "no propagation of the wave (the velocity will be zero). The tension\n", "_along_ the string is provided by the wall, but the tension\n", "_transverse_ to the string at the wall must be zero (otherwise\n", "the wall would move up and down). We can therefore write that: \n", "\n", "\\begin{eqnarray}\n", " T\\left( \\frac{\\partial \\psi_i}{\\partial x}\\right)_{x=L} &+& T\\left( \\frac{\\partial \\psi_r}{\\partial x}\\right)_{x=L} = 0\\\\\n", " \\Rightarrow T\\left( \\frac{\\partial \\psi_i}{\\partial x}\\right)_{x=L} &=& - T\\left( \\frac{\\partial \\psi_r}{\\partial x}\\right)_{x=L}\\\\\n", " \\left( \\frac{\\partial \\psi_i}{\\partial x}\\right)_{x=L} &=& -\\left( \\frac{\\partial \\psi_r}{\\partial x}\\right)_{x=L}\n", "\\end{eqnarray}\n", "\n", "So there must be a 180$^\\circ$ phase change on reflection; this is\n", "another way of saying that the reflected wave has the opposite sign to\n", "the incoming wave. But what happens now if, instead of a solid wall,\n", "we have _another_ string with a different mass per unit length ?\n", "To be clear, we will assume that we have two strings of lengths $L_1$\n", "and $L_2$ joined at $x=0$ held under tension T. The first string has\n", "mass density $\\mu_1$, impedance $Z_1 = \\sqrt{T\\mu_1}$ and has a driver\n", "at its free end ($x=-L_1$). The second string has mass density\n", "$\\mu_2$, impedance $Z_2 = \\sqrt{T\\mu_2}$ and has perfect termination\n", "(i.e. a drag term with impedance $Z_2$) at $x=L_2$. \n", "\n", "Now consider an incident wave, starting at $x=-L_1$ and moving towards\n", "the joining point at $x=0$. As it propagates, there is a transverse\n", "force on the string given by: \n", "\n", "\\begin{equation}\n", "-T\\left(\\frac{\\partial \\psi}{\\partial x} \\right)= Z\\left(\\frac{\\partial \\psi}{\\partial t} \\right)\n", "\\end{equation}\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We assume, generally, that $\\psi = \\psi_i + \\psi_r, x\\le 0$. Exactly\n", "at the join, the wavefunctions on the two sides must equal, so $\\psi_i(0,t)\n", "+ \\psi_r(0,t) = \\psi_t(0,t)$.\n", "\n", "At the joining point, the drag exerted by the second string _on_\n", "the first string will be given by its impedance multiplied by the\n", "transverse velocity of the string:\n", "\n", "\\begin{equation}\n", " F_{\\mathrm{drag}} = Z_2 \\frac{\\partial \\psi_t}{\\partial t} = Z_2 \\frac{\\partial }{\\partial t}\\left(\\psi_i + \\psi_r\\right) = Z_2 \\left(\\frac{\\partial \\psi_i}{\\partial t} + \\frac{\\partial \\psi_r}{\\partial t}\\right)\n", "\\end{equation}\n", "\n", "This force will be balanced by the transverse force from the string:\n", "\n", "\\begin{equation}\n", " -T\\frac{\\partial \\psi}{\\partial x} = -T\\left(\\frac{\\partial \\psi_i}{\\partial x} + \\frac{\\partial \\psi_r}{\\partial x}\\right) = Z_1 \\left(\\frac{\\partial \\psi_i}{\\partial t} - \\frac{\\partial \\psi_r}{\\partial t}\\right)\n", "\\end{equation}\n", "Note that the change of sign between the partial derivatives comes\n", "when we use the travelling wave equation to relate the spatial and\n", "time derivatives: the incoming wave gives a minus sign (which cancels\n", "the minus sign outside the bracket) while the reflected wave gives a\n", "plus sign. We can now derive a condition relating the incident and\n", "reflected waves, by equating the two forces: \n", "\n", "\\begin{eqnarray}\n", " Z_1 \\left(\\frac{\\partial \\psi_i}{\\partial t} - \\frac{\\partial \\psi_r}{\\partial t}\\right) &=& Z_2 \\left(\\frac{\\partial \\psi_i}{\\partial t} + \\frac{\\partial \\psi_r}{\\partial t}\\right)\\\\\n", " (Z_1 - Z_2)\\left(\\frac{\\partial \\psi_i}{\\partial t}\\right) &=& (Z_1 + Z_2) \\left(\\frac{\\partial \\psi_r}{\\partial t}\\right)\\\\\n", " \\left(\\frac{\\partial \\psi_r}{\\partial t}\\right) &=& \\frac{Z_1 - Z_2}{Z_1 + Z_2} \\left(\\frac{\\partial \\psi_i}{\\partial t}\\right)\n", "\\end{eqnarray}\n", "\n", "If we integrate both sides with respect to time, we find that:\n", "\\begin{equation}\n", " \\psi_r(0,t) = \\frac{Z_1 - Z_2}{Z_1 + Z_2} \\psi_i(0,t)\n", "\\end{equation}\n", "This gives the relation between $\\psi_i$ and $\\psi_r$ at the joining\n", "point of the two strings. As both waves are travelling waves, we can\n", "relate the value at one time and place to the value at another time\n", "and place: \n", "\\begin{eqnarray}\n", " \\psi_i(-l,t-l/c) &=& \\psi_i(0,t)\\\\\n", " \\psi_r(-l,t+l/c) &=& \\psi_r(0,t) = R\\psi_i(0,t) = R \\psi_i(-l,t-l/c)\\\\\n", " R &=& \\frac{Z_1 - Z_2}{Z_1 + Z_2}\n", "\\end{eqnarray}\n", "In other words, the reflected wave at $x=-l$ and $t=t+l/c$ is the\n", "same as the incident wave at the same position but at a time $2l/c$ in\n", "the past, and scaled by $R$, which we call the _reflection\n", " coefficient_. Notice that the time delay is just the time it takes\n", "for the wave to travel along the string and back again. \n", "\n", "We can also say something about the wave in the second string. We\n", "must have the following boundary condition: \n", "\n", "\\begin{equation}\n", " \\psi_i(0,t) + \\psi_r(0,t) = \\psi_t(0,t),\n", "\\end{equation}\n", "\n", "where $\\psi_t$ is the transmitted wave. This must be so, otherwise\n", "there will be a discontinuity in the string. So the transmitted wave\n", "is related to the incident wave by the following formula: \n", "\n", "\\begin{eqnarray}\n", " \\psi_t(0,t) &=& \\psi_i(0,t) + R\\psi_i(0,t)\\\\\n", " &=& (1+R) \\psi_i(0,t) = T \\psi_i(0,t)\\\\\n", " T &=& 1+R = \\frac{2Z_1}{Z_1 + Z_2}\n", "\\end{eqnarray}\n", "\n", "where $T$ is called the _transmission coefficient_. Notice that\n", "the reflection coefficient will take values between -1 and 1, while\n", "the transmission coefficient will take values between 0 and 2: \n", "\n", "\\begin{eqnarray}\n", " -1 &\\le& R \\le 1\\\\\n", " 0 &\\le& T \\le 2\n", "\\end{eqnarray}\n", "\n", "If there is a single string terminated with a very large impedance (a\n", "solid wall, as before, so $Z_2 \\gg Z_1$) then we will have $R =\n", "-Z_2/Z_2 = -1$ and we get the phase change we saw before (and no\n", "transmission). If the string is terminated with a very small\n", "impedance (a free end, for instance, so that $Z_1 \\gg Z_2$) then we\n", "will have $R = Z_1/Z_1 = 1$ and no phase change in the reflected wave.\n", "When there are two strings, then in the limit of the second string\n", "having negligible impedance the transmitted wave will have twice the\n", "amplitude of the incident wave, and the reflected wave will have the\n", "same height as the incident wave. When the two impedances are\n", "matched, it will be as if there was only one string ($R=0, T=1$). \n", "\n", "In the figure below, we plot a system with two impedances (it is assumed that these are two strings with different masses per unit length). You should try changing the impedances and rerunning the code to see the effect on the coefficients and behaviour of the system. When we move away from $t=0$ some interesting changes happen - but they are not wrong. Remember that a large amplitude in the transmitted wave may be because the impedance is small: it is easy to excite a wave on a string with small impedance." ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig = figure(figsize=[12,3])\n", "# Add subplots: number in y, x, index number\n", "ax = fig.add_subplot(121,autoscale_on=False,xlim=(-10,10),ylim=(-2,2))\n", "ax2 = fig.add_subplot(122,autoscale_on=False,xlim=(-10,10),ylim=(-2,2))\n", "# Set up limits on the graph: we will plot from -10 to 10, with the boundary at 0\n", "xmin = -10\n", "xmax = 10\n", "# Create x arrays for x<0 and x>0\n", "xL = linspace(xmin,0.0,1000)\n", "xR = linspace(0.0,xmax,1000)\n", "# System parameters: tension, masses per unit length, frequency, amplitude of incoming wave\n", "T = 1.0\n", "mu1 = 1.0\n", "mu2 = 2.0\n", "omega = 1.0\n", "A = 1.0\n", "# The time at which we visualise can have an important effect, and produce surprising results\n", "time = 0.0\n", "# Derive speeds, wavenumbers, impedances\n", "c1 = sqrt(T/mu1)\n", "c2 = sqrt(T/mu2)\n", "k1 = omega/c1\n", "k2 = omega/c2\n", "Z1 = sqrt(T*mu1)\n", "Z2 = sqrt(T*mu2)\n", "# Ra and Ta are reflection and transmission coefficients (to avoid confusion with tension T above)\n", "Ra = (Z1-Z2)/(Z1+Z2)\n", "Ta = 1+Ra\n", "print \"Z1 and Z2 are: \",Z1,Z2\n", "print \"R and T are: \",Ra,Ta\n", "# Create psi_i, psi_r and psi_t (include time - note that psi_r travels in negative x direction)\n", "left_i = A * cos(k1*xL-omega*time)\n", "left_r = A * Ra*cos(k1*xL+omega*time)\n", "# left is the total wave for x<0\n", "left = left_i + left_r\n", "# right is the wave for x>0\n", "right = A*Ta*cos(k2*xR-omega*time)\n", "# Plot total waves in left plot\n", "ax.plot(xL,left,label=r\"$\\psi_i+ \\psi_r$\")\n", "ax.plot(xR,right,label=r\"$\\psi_t$\")\n", "ax.legend()\n", "# Plot individual waves in right plot\n", "ax2.plot(xL,left_i,label=r\"$\\psi_i$\")\n", "ax2.plot(xR,right,label=r\"$\\psi_t$\")\n", "ax2.plot(xL,left_r,label=r\"$\\psi_r$\")\n", "ax2.legend()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Z1 and Z2 are: 1.0 1.41421356237\n", "R and T are: -0.171572875254 0.828427124746\n" ] }, { "metadata": {}, "output_type": "pyout", "prompt_number": 59, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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AUN+2PiqVqYTj94+L0r7QgmOC0de9r+BLMPINbDAQO67uMOuZGFO2aRMwYABQ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\nJhG5mcK4nS8/WSuOxo8HVqyQr//4eOD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"text": [ "" ] } ], "prompt_number": 59 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The phase velocities and wavelengths on either side of an interface\n", "between two media will be different, but the frequencies will be the\n", "same, provided that the interface has no mechanism for driving waves.\n", "We can understand by thinking about the effect of the interface on the\n", "second medium: it will act as a harmonic driving force at frequency\n", "$\\omega$. Consider a join between two strings of different mass per\n", "unit length (but under the same tension) to be specific. Then if we\n", "send a wave with frequency $\\omega$ down the first string, all points\n", "on the string will oscillate harmonically with frequency $\\omega$.\n", "This must be true of the junction, which will then excite waves of the\n", "same frequency in the second string. So we have: \n", "\n", "\\begin{eqnarray}\n", " \\omega_1 &=&\\omega_2 = \\omega\\\\\n", " \\nu_1 &=& \\nu_2 = \\frac{\\omega}{2\\pi}\\\\\n", " c_1 &=& \\sqrt{\\frac{T}{\\mu_1}}\\\\\n", " k_1 &=& \\frac{\\omega_1}{c_1} = \\frac{\\omega}{c_1}\\\\\n", " \\lambda_1 &=& \\frac{c_1}{\\nu}\\\\\n", " c_2 &=& \\sqrt{\\frac{T}{\\mu_2}}\\\\\n", " k_2 &=& \\frac{\\omega_2}{c_2} = \\frac{\\omega}{c_2}\\\\\n", " \\lambda_2 &=& \\frac{c_2}{\\nu}\\\\\n", "\\end{eqnarray}\n", "\n", "Later in the course we will encounter situations where the frequency\n", "and wavelength are not so simply related (called dispersive systems)\n", "but even for these materials frequencies are conserved across\n", "boundaries. \n", "\n", "We can summarise the results on driving waves, terminating, and\n", "behaviour at interfaces as follows: \n", "\n", "* If we want to drive a wave along a semi-infinite string, then the driver must supply a force proportional to the _transverse_ velocity of the end of the string it is driving. The constant of proportionality is known as the _characteristic impedance_. \n", "* If we want to terminate a finite, driven string so that the same wave motion as would be found on an infinite string is supported, it must be terminated with an impedance equal to the characteristic impedance of the string. \n", "* If a string (or any medium) is not terminated with the correct impedance then reflection as well as transmission will occur at the interface according to the reflection and transmission coefficients given above." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Standing Waves" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So far, we have considered a stretched string with a driver at one end\n", "and some form of impedance at the other end. Now we will consider a\n", "set-up where the string is _fixed at both ends_; we will assume\n", "that there is some means of driving a wave in the string (for instance\n", "a guitar pick or a violin bow). This is another example of boundary\n", "conditions which we can implement; again, we must have both forms of\n", "wave: $\\psi = f(x-ct) + g(x+ct)$. If the string has length $L$ then\n", "we can write: \n", "\n", "\\begin{eqnarray}\n", " \\psi(0,t) &=& \\psi(L,t) = 0\\\\\n", " \\left(\\frac{\\partial \\psi}{\\partial t}\\right)_{x=0} &=& \\left(\\frac{\\partial \\psi}{\\partial t}\\right)_{x=L} = 0\n", "\\end{eqnarray}\n", "\n", "Let us consider the general wave solution and assume that we will have\n", "a sinusoidal solution of some kind. Then we can write, quite\n", "generally, \n", "\n", "\\begin{equation}\n", " \\psi(x,t) = Ae^{i(\\omega t-kx)} + Be^{i(\\omega t+kx)}\n", "\\end{equation}\n", "Note that I've written the two so that the time variation shares the\n", "same sign and the x variation differs. This is just as general a\n", "solution of the wave equation, and makes the maths slightly easier.\n", "What can we learn from the boundary conditions ? Let's look at $x=0$\n", "first. \n", "\n", "\\begin{eqnarray}\n", " \\psi(0,t) &=& Ae^{i\\omega t} + Be^{i\\omega t} = 0\\\\\n", " \\Rightarrow A &=& -B\\\\\n", " \\psi(x,t) &=& Ae^{i\\omega t}\\left( e^{ikx} - e^{-ikx}\\right) \\\\\n", " &=& 2iAe^{i\\omega t}\\sin(kx)\n", "\\end{eqnarray}\n", "\n", "So we've shown something quite important about the form of the wave\n", "just from the first condition; notice that the minus sign between the\n", "two components is exactly what we'd expect for a wave reflected from a\n", "solid wall. Now let's consider the boundary condition at $x=L$: \n", "\n", "\\begin{eqnarray}\n", " \\psi(L,t) &=& 2iAe^{i\\omega t}\\sin(kL) = 0\\\\\n", " \\Rightarrow kL &=& n\\pi\n", "\\end{eqnarray}\n", "where $n$ is an integer, as we know that sin has zeroes for integer\n", "multiples of $\\pi$. So we have a series of solutions for $k$ which\n", "will all fit the boundary conditions. We can write: \n", "\\begin{eqnarray}\n", " k_n &=& \\frac{n\\pi}{L}\\\\\n", " \\lambda_n &=& \\frac{2\\pi}{k_n} = \\frac{2L}{n}\\\\\n", " n&=& 1, 2, 3, \\dots\n", "\\end{eqnarray}\n", "So there are only a certain set of wavelengths that will fit onto the\n", "string; this makes sense, as we have imposed a certain length scale on\n", "the system, and should expect the resulting solutions to fit into that\n", "length. In fact, if we take the idea of normal modes from\n", "Sec.~2.5 to its continuous limit, we find\n", "that the allowed solutions for the string are the normal modes of the\n", "system. \n", "\n", "The first five standing waves for a string fixed at both ends are plotted below, though you should experiment with the parameters and see what happens." ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig = figure(figsize=[12,7])\n", "# Set length scale\n", "L = 5.0\n", "# We will put the subplots into an array, ax\n", "ax = []\n", "# Define x coordinates and omega\n", "x = linspace(0,L,1000)\n", "omega = 1.0\n", "# Loop over first five modes, n\n", "for n in range(1,6):\n", " # Create subplot; we want 5 in y and 1 in x, with incremented index - spn gives this\n", " spn = 510+n\n", " # Plot mode n\n", " ax.append(fig.add_subplot(spn,autoscale_on=False,xlim=(0,L),ylim=(-1.1,1.1)))\n", " # Plot at a number of times to show how the wave changes\n", " for t in range(4):\n", " ax[n-1].plot(x,sin(n*pi*x/L)*sin(omega*pi*t/2.0))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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+vh5Xr17NdjcIIYQQQsgSVldXhytXrtz1mJwJyIQQQgghhOQCWhiUEEIIIYSQ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\nU8iobqqmrKGMvNo8zsvOs/v8blLLU6ltq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8rPMGfHHGqaavhk9Cfc5HuTrkPSe3/k/8Hc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\nWUGBUGu1ug7pmqg1arHs2DLh/J6zeGXfK6JR2ajrkLqE8oZy8chPjwjPJ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"text": [ "" ] } ], "prompt_number": 60 }, { "cell_type": "markdown", "metadata": {}, "source": [ " The patterns along the string\n", "are important, and we can define: \n", "\n", "* _Nodes_ Where the wave amplitude is zero (these points are stationary at all times) \n", "* _Antinodes_ Where the wave amplitude is a maximum\n", "\n", "There are $n$ maxima or anti-nodes, and $n-1$ stationary points or\n", "nodes for mode $n$. Since the speed of the wave depends on the\n", "material properties of the system (the tension and mass density in a\n", "string), the frequencies of the waves must also be arranged in a\n", "series which depends on $n$: \n", "\\begin{eqnarray}\n", " \\omega_n &=& c k_n = \\frac{n\\pi c}{L}\\\\\n", " \\nu_n &=& \\frac{\\omega_n}{2\\pi} = \\frac{nc}{2L}\n", "\\end{eqnarray}\n", "These are the _normal frequencies_ which arise because of the\n", "boundary conditions imposed on the system. Notice that, for this\n", "system (which is rather special), the normal frequencies are integer\n", "multiples of the first frequency. In general, the integer multiples\n", "of a fundamental frequency are called the _harmonics_. \n", "\n", "Notice that the standing waves arise because of _interference_\n", "between two waves moving in opposite directions. The formation of\n", "standing waves occurs because of _constructive_ interference\n", "between waves moving in opposite directions. " ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Resonance" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A string fixed at both ends can support a series of different waves;\n", "the lowest frequency wave (with longest wavelength) is called the\n", "_fundamental_ frequency. In the same way, most physical systems\n", "will have natural frequencies as we saw in the case of the harmonic\n", "oscillator. These frequencies are also known as resonant frequencies,\n", "as an excitation applied at this frequency will generate a resonance;\n", "as we mentioned briefly in Sec. 2.3, the amplitude of a\n", "damped, driven harmonic oscillator will be at a maximum when the\n", "driving frequency equals the natural or resonant frequency. \n", "\n", "If a complex excitation is applied to an object, causing it to\n", "vibrate, it will tend to pick out its resonant frequencies, as these\n", "will respond with a large amplitude. A sharp impulse (like a kick or\n", "a whack from a stick) delivered to a simple oscillator will give a\n", "motion which is somewhat chaotic initially but will settle down to an\n", "oscillation at the natural frequency. The impulse consists of many\n", "frequencies (which can be investigated with Fourier analysis) but the\n", "oscillator will only respond strongly at its resonant frequency. Most\n", "objects which vibrate will have multiple resonant frequencies\n", "(depending on the boundary conditions which they impose). \n" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Nodes and Antinodes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The wave which is supported on a string fixed at both ends have a very\n", "different form to those we used above: the time variation has been\n", "separated from the spatial variation: \n", "\\begin{equation}\n", " \\psi(x,t) = \\mathrm{Re}\\left[2iAe^{i\\omega t}\\sin(kx)\\right] = -2A \\sin(\\omega t) \\sin(kx)\n", "\\end{equation}\n", "So each point on the string is _in phase_ with all other points\n", "on the string, and they undergo simple harmonic motion, with the\n", "amplitude of the motion depending on the position along the string.\n", "The points on the string where $kx = n\\pi$ for $n$ an integer will\n", "have zero amplitude (as $\\sin(n\\pi) = 0$); these are the nodes. The\n", "points on the string where $kx = (n+\\frac{1}{2})\\pi$ for $n$ an\n", "integer will have maximum amplitude of $2A$. \n", "\n", "The positions $x$ of the nodes and antinodes are found by substituting\n", "$k = 2\\pi/\\lambda$ into the expressions given above: \n", "\n", "\\begin{eqnarray}\n", " x_{\\mathrm{node}} &=& \\frac{n\\pi}{2\\pi/\\lambda} = n\\frac{\\lambda}{2}\\\\\n", " x_{\\mathrm{antinode}} &=& \\frac{\\left(n + \\frac{1}{2}\\right)\\pi}{2\\pi/\\lambda} = \\left(n+\\frac{1}{2}\\right)\\frac{\\lambda}{2}\n", "\\end{eqnarray}\n", "\n", "The nodes are separated from each other by half a wavelength (which is\n", "easy to see by calculating $x(n=1) - x(n=0)$), and the anti-nodes are\n", "also separated from each other by half a wavelength (this is by\n", "definition: these are the zeroes and extrema of a sinusoidal function\n", "and must be separated by half a wavelength). Each node is separated\n", "by $\\lambda/4$ from the nearest anti-nodes. \n", "\n", "As an example, consider a piano string (this is an oversimplification\n", "- pianos have two or three strings for each note). The mass per unit\n", "length is typically around 0.01 kg/m and the tension is around 800N\n", "(equivalent to the gravitational force exerted by the mass of an\n", "average person). The velocity of waves on this string will be\n", "$\\sqrt{800/0.01} = 283$m/s. If the wire is 0.6m long and the ends are\n", "fixed, then the lowest allowed wavelength will be 1.2m (with other\n", "waves with wavelengths 0.6m and 0.4m and so on also allowed). The\n", "frequencies of these waves will be: \n", "\n", "\\begin{eqnarray}\n", " f_1 &=& \\frac{c}{\\lambda_1} = 236 \\mathrm{Hz}\\\\\n", " f_2 &=& 472 \\mathrm{Hz}\\\\\n", " f_3 &=& 708 \\mathrm{Hz}\n", "\\end{eqnarray}\n", "The fundamental will be just below middle C (which is about 262 Hz)." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Harmonics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The fundamental frequency for an ideal vibrating string will arise\n", "from the longest wavelength which can be supported. This is\n", "$\\lambda_1 = 2L$ for a string of length $L$. We then write: \n", "\\begin{eqnarray}\n", " f_1 &=& \\frac{c}{\\lambda_1} = \\frac{c}{2L}\\\\\n", " f_n &=& \\frac{2}{\\lambda_n} = \\frac{nc}{2L}\n", "\\end{eqnarray}\n", "for $n=1,2,3,\\ldots$ where $c = \\sqrt{T/\\mu}$. A \\emph{harmonic} is\n", "simply a vibration at an integer multiple of the fundamental\n", "frequency. Systems with the \\emph{same} boundary conditions at both\n", "ends (e.g. fixed strings, open air columns etc.) will vibrate with all\n", "harmonics of the fundamental frequency, while systems with different\n", "boundary conditions (i.e. one end fixed and one free) will vibrate\n", "with only the odd harmonics. Most musical instruments will produce\n", "some harmonics when the fundamental frequency is excited (and it is\n", "also possible to excite the harmonics only, for instance by\n", "overblowing a wind instrument or inducing a node on a stringed\n", "instrument by touching the string lightly). " ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Other Boundary Conditions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is worth noting that there are other ways to set up standing waves.\n", "If a continuous wave (a sinusoidal wave, for example) is propagated\n", "along a semi-infinite string towards a fixed end, then it will reflect\n", "with a phase change of $\\pi$ (or a change in sign). If we take the\n", "incoming wave to be $\\psi_i = A \\cos(kx - \\omega t +\\phi)$ the\n", "reflected wave will be $\\psi_r = -A\\cos(kx+\\omega t +\\phi)$. Then we\n", "will find: \n", "\n", "\\begin{eqnarray}\n", " \\psi(x,t) &=& \\psi_i(x,t) + \\psi_r(x,t) \\\\\n", " &=& A \\cos(kx - \\omega t) - A \\cos(kx + \\omega t)\\\\\n", " &=& -2A\\sin(kx)\\sin(\\omega t + \\phi)\n", "\\end{eqnarray}\n", "which is exactly the form we saw above.\n", "\n", "This suggests that it is worth examining other boundary conditions on\n", "waves, to explore the full range of standing waves. Instead of a\n", "fixed end (or a node) we could allow the medium to have an antinode\n", "(or free end) at one or both ends. This is quite common when thinking\n", "about sound waves and we will consider pipes in detail in\n", "the section on standing waves in a fluid. For now, let us consider what an\n", "antinode at both ends would mean (think of holding a thin steel ruler\n", "lightly in the centre and wiggling it up and down: you impose a node\n", "at the centre but nothing at the ends). This is equivalent to setting\n", "$\\partial \\psi/\\partial x = 0$ (think about the transverse component\n", "of the tension - we are setting it to zero as there is no constraint on the system at the ends).\n", "\n", "We will take advantage of our knowledge of the system to suggest the form:\n", "\\begin{eqnarray}\n", " \\psi(x,t) = 2A\\cos(kx)\\sin(\\omega t)\n", "\\end{eqnarray}\n", "We will again impose the condition that $kx = n\\pi$ at $x=0$ and $x=L$\n", "for $n$ an integer, but this time we are forcing an antinode to be at\n", "the boundaries. The allowed series of wavelengths will then be given\n", "by: \n", "\\begin{eqnarray}\n", " k_n &=& \\frac{n\\pi}{L}\\\\\n", " \\Rightarrow \\lambda_n &=& \\frac{2\\pi}{k_n} = \\frac{2L}{n}\n", "\\end{eqnarray}\n", "which is the same set of wavelengths (really all we've done to the\n", "system is introduce a phase shift of $\\pi/2$). We'll consider the\n", "effect of a free end and a fixed end when we look at sound waves in\n", "pipes. \n", "\n", "We can plot these waves in exactly the same way as for the fixed boundary conditions, and this is done below." ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig = figure(figsize=[12,7])\n", "# Set length scale\n", "L = 5.0\n", "# We will put the subplots into an array, ax\n", "ax = []\n", "# Define x coordinates and omega\n", "x = linspace(0,L,1000)\n", "omega = 1.0\n", "# Loop over first five modes, n\n", "for n in range(1,6):\n", " # Create subplot; we want 5 in y and 1 in x, with incremented index - spn gives this\n", " spn = 510+n\n", " # Plot mode n\n", " ax.append(fig.add_subplot(spn,autoscale_on=False,xlim=(0,L),ylim=(-1.1,1.1)))\n", " # Plot at a number of times to show how the wave changes\n", " for t in range(4):\n", " ax[n-1].plot(x,cos(n*pi*x/L)*sin(omega*pi*t/2.0))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, 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8N4/EkOrM3DMgnzx5ck7/sDabDQMDA+L2wMAAysrKpj0+/sEHc/p5ZPFZCi9u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2aJQyTI/8JgNHBYfpgfLvzAD+k/YJAMPNT5IR6+9WE6+HRo1liE30iSxIGaGlYXF/NDaSkB9vaM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\nkUGNWs3GoCAGdIK/cUJxAov2LcLE0IRP7/+UMLcwfYfU5cQVxbFw70IsT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