add plane_wave.ipynb #12
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plane_wave.ipynb
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| " To the extent possible under law,\n", | ||
| " <span rel=\"dct:publisher\" resource=\"[_:publisher]\">the person who associated CC0</span>\n", | ||
| " with this work has waived all copyright and related or neighboring\n", | ||
| " rights to this work. Author: <a href=\"https://github.com/fs446\">https://github.com/fs446</a>\n", |
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If you want to include authorship information (which I specifically chose not to do, in order to lower the bar for contributions), you can use the tool at https://creativecommons.org/choose/zero/waiver. Mentioning your name here does not change the obligations of users (they still have none).
If you want to legally require people to mention your name when they reproduce/change the materials, you should use CC-BY instead.
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Thanks for this hint! I removed the autorship, such that we are consistent within this course. I only liked the idea, that interested people find autorship information directly in the notebook and don't need to trace this in the git repo (where this information is encoded anyway). However, I did not figure the implications of different licensing models. So making it most convenient for re-usage is nice to me too.
plane_wave.ipynb
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That's obviously a matter of taste, but I prefer kebab-case over snake_case for file names, unless it's not technically possible.
Either way, it would be good to be consistent.
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An old bad habit presumably originating from my assembler coding days :-) Changed for consistency to plane-wave.ipynb, which I then also have done for greens-functions.ipynb (I hope there is no dependency on this in the other notebooks).
plane_wave.ipynb
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| "source": [ | ||
| "# 1. Plane wave in free field\n", | ||
| "\n", | ||
| "We play around with the plane wave solution $p \\,\\propto\\, \\mathrm{e}^{\\mathrm{j}(-k_x x - k_y y + \\omega t)}$ of the linear, homogeneous wave equation\n", |
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Maybe "linear and homogeneous" or just "linear homogeneous"?
plane_wave.ipynb
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| "\n", | ||
| "We play around with the plane wave solution $p \\,\\propto\\, \\mathrm{e}^{\\mathrm{j}(-k_x x - k_y y + \\omega t)}$ of the linear, homogeneous wave equation\n", | ||
| "\n", | ||
| "$$\\mathrm{div}\\,\\mathrm{grad}\\,p(\\mathbf{x},t) - \\frac{1}{c^2} \\frac{\\partial^2 p(\\mathbf{x},t)}{\\partial t^2} = 0$$\n", |
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It's a matter of taste but I would use the compact Laplacian notation and define it in the following text using div and grad.
plane_wave.ipynb
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| "source": [ | ||
| "# 1. Plane wave in free field\n", | ||
| "\n", | ||
| "We play around with the plane wave solution $p \\,\\propto\\, \\mathrm{e}^{\\mathrm{j}(-k_x x - k_y y + \\omega t)}$ of the linear, homogeneous wave equation\n", |
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Is there any reason of using propto instead of introducing an amplitude like p_A in the code below?
plane_wave.ipynb
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| "outputs": [], | ||
| "source": [ | ||
| "c = 343 # m/s, speed of sound\n", | ||
| "wave_length = 1 # m\n", |
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How about starting with frequency f or angular frequency w, as mentioned in the text above?
In my opinion, it will better highlight the relation of temporal and spatial frequencies (i.e. dispersion relation).
It seems a bit weird in the code below, that the angular frequency/speed-of-sound is computed from 1/wavelength.
plane_wave.ipynb
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| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "col_tick = np.linspace(-pA, +pA, 255, endpoint=True)\n", |
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This looks really cool!
My little concern is that the students might understand 2D plane wave as something like a surface wave, which is two different physical phenomena.
plane_wave.ipynb
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| "source": [ | ||
| "# 3. Plane wave with certain boundary conditions lead to a standing wave\n", | ||
| "\n", | ||
| "We consider 1D radiation along $x$-axis. Hence, $k_x^2 = \\left(\\frac{\\omega}{c}\\right)^2$, $k_y=$, $k_z=0$.\n", |
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k_y = k_z = 0 (without comma) or k_y=0, k_z=0
plane_wave.ipynb
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| "\n", | ||
| "We consider 1D radiation along $x$-axis. Hence, $k_x^2 = \\left(\\frac{\\omega}{c}\\right)^2$, $k_y=$, $k_z=0$.\n", | ||
| "\n", | ||
| "At $-l$ (with $l>0$), i.e. at some point on the negative $x$-axis, there is an ideal membrane located, which injects the harmonic velocity $v_A$ into a (long, thin) tube.\n", |
plane_wave.ipynb
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| "# boundary condition for rigid wall\n", | ||
| "p_cpx = 2*pA * np.cos(kx*x)\n", | ||
| "v_cpx = 2*pA * -1j / (rho0*c) * np.sin(kx*x)\n", | ||
| "\n", |
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Would be helpful to comment that the time-harmonic term (phasor) is not included and will be multiplied in the following code.
plane_wave.ipynb
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| "\n", | ||
| "\n", | ||
| "ax.set_xlabel('x / m')\n", | ||
| "ax.set_ylabel(r'$\\frac{p}{pA}$, $\\frac{v}{pA}\\cdot\\rho_0 c$')\n", |
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How about adding a second y-label (for velocity) on the right side.
plane_wave.ipynb
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| " frames=np.arange(n_periods*n_samples_per_period+4),\n", | ||
| " blit=True, interval=50,\n", | ||
| " repeat=False)\n", | ||
| "plt.show()" |
* Added visualization task for modes * proofreading * Deleted solution part from the task. Minor changes in written text. * Added introduction. * Descriptional improvements at 2d case. * Inserted the equations to show that the boundary conditions are satisfied. * some mods/adds to modal stuff * Deleted time dependencies in 2d case. --------- Co-authored-by: Frank Schultz <[email protected]>
added a Jupyter notebook for