From e20d3258a8f49168c8de34356ebf1ed9ad38c284 Mon Sep 17 00:00:00 2001 From: Luca Zoppetti Date: Wed, 20 Mar 2024 14:28:07 +0100 Subject: [PATCH] fix lec8 --- .../screenshots/2024-03-20-09-22-51.png | Bin 17460 -> 0 bytes .../screenshots/2024-03-20-09-26-28.png | Bin 6430 -> 6053 bytes .../screenshots/2024-03-20-09-46-35.png | Bin 30343 -> 39380 bytes .../screenshots/2024-03-20-09-58-18.png | Bin 6315 -> 24910 bytes .../screenshots/2024-03-20-09-58-18.png.png | Bin 24910 -> 0 bytes tex/waves/lectures/lec_8.tex | 20 ++++++------------ 6 files changed, 6 insertions(+), 14 deletions(-) delete mode 100644 tex/waves/figures/screenshots/2024-03-20-09-22-51.png delete mode 100644 tex/waves/figures/screenshots/screenshots/2024-03-20-09-58-18.png.png diff --git a/tex/waves/figures/screenshots/2024-03-20-09-22-51.png b/tex/waves/figures/screenshots/2024-03-20-09-22-51.png deleted file mode 100644 index c2efa2b1d356a69aa58c610b5fdee6e4f98e6dcd..0000000000000000000000000000000000000000 GIT binary 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z-?Y%O6bB!JP&oC4FVOh{O#sdOgm|04 zRohPinibmp%c+;#xwH%nI;_9NpPzd^)x^YcJpGVngO^=^WD{mNnlwsQsXopI0GFt7 pcpiBq|6`&4FBN5?Uj2`@Fr1s7y(QcR_zwi6H;N#IMmfvy{|6g6$?^aI diff --git a/tex/waves/lectures/lec_8.tex b/tex/waves/lectures/lec_8.tex index 5193f26..8e6ab52 100644 --- a/tex/waves/lectures/lec_8.tex +++ b/tex/waves/lectures/lec_8.tex @@ -1,18 +1,11 @@ \section{Riflessione e trasmissione} -\lecture{8}{20 marzo 2024} - -Oggi studiamo i mezzi non omogenei per la trasmissione di onde. In questi mezzi può avvenire il fenomeno della riflessione, al contrario dei mezzi omogenei in cui l'onda si propaga senza cambiare forma. +Oggi studiamo i mezzi non omogenei per la trasmissione di onde. In questi mezzi può avvenire il fenomeno della riflessione, al contrario dei mezzi omogenei in cui l'onda si propaga senza cambiare forma. In generale, nel passaggio di un'onda fra due mezzi diversi si possono avere un'onda riflessa e un'onda trasmessa: -\begin{figure}[H] - \centering - \includegraphics[width=0.8\textwidth]{screenshots/2024-03-20-09-22-51.png} -\end{figure} - -In generale, nel passaggio di un'onda fra due mezzi diversi si possono avere un'onda riflessa e un'onda trasmessa: +\lecture{8}{20 marzo 2024} \begin{figure}[H] \centering - \includegraphics[width=0.8\textwidth]{screenshots/2024-03-20-09-25-33.png} + \includegraphics[width=0.6\textwidth]{screenshots/2024-03-20-09-25-33.png} \end{figure} Consideriamo ora una corda elastica con due densità diverse (la discontinuità è in \(x=0\)): @@ -79,7 +72,7 @@ \subsection{Analisi energetica} Usiamo quanto trovato ieri per trovare l'intensità delle tre onde: \begin{figure}[H] \centering - \includegraphics[width=0.8\textwidth]{screenshots/screenshots/2024-03-20-09-58-18.png.png} + \includegraphics[width=0.8\textwidth]{screenshots/2024-03-20-09-58-18.png} \end{figure} Da cui si ricava che la somma delle intensità dell'onda trasmessa e dell'onda riflessa è uguale all'intensità dell'onda incidente, è un modo di scrivere la conservazione dell'energia! \begin{figure}[H] @@ -106,9 +99,8 @@ \subsection{Analisi energetica} Si vede immediatamente che la massima onda trasmessa si ha per \(I_r=0 \implies A_r = 0 \implies Z_1 = Z_2\). La condizione \(Z_1\thickapprox Z_2\) è nota in fisica con il termine di \emph{raccordo delle impedenze}. In generale è più semplice ottenere questo risultato con variazioni lente (non brusche come appena studiato) dei parametri della corda: \begin{figure}[H] \centering - \includegraphics[width=0.8\textwidth]{screenshots/2024-03-20-10-13-59.png} + \includegraphics[width=0.5\textwidth]{screenshots/2024-03-20-10-13-59.png} \end{figure} -%TODO: una figura incollata non è poi stata usata. Modifica pfig per prendere un parametro per la larghezza, tipo 0.6pfig \section{Onde stazionarie} Studiamo una corda fissata a un estremo, che può essere pensato come una corda con \(\mu _0 \to \infty \). Consideriamo un'onda regressiva proveniente dalla regione \(x>0\): @@ -156,7 +148,7 @@ \subsection{Corda vincolata a due estremi} Le frequenze che si ottengono dalle oscillazioni di modo normale sono dette "frequenze proprie" o "autofrequenze". Qualunque onda che viaggia su una corda vincolata ai due estremi può essere espresse come combinazione lineare di armoniche fondamentali: \begin{figure}[H] \centering - \includegraphics[width=0.8\textwidth]{screenshots/2024-03-20-10-55-47.png} + \includegraphics[width=0.5\textwidth]{screenshots/2024-03-20-10-55-47.png} \end{figure} \paragraph{Una chitarra} Nella chitarra classica ci sono sei corde vincolate di diverso materiale: tipicamente tre sono di metallo e tre di nylon, avendo densità diverse permettono di coprire uno spettro più ampio di frequenze.