Standing waves in air

Standing waves in a open and half-closed pipes. Also see standing waves in a flute, traveling waves in air, and more related figures in the Music category.

Pressure and displacement

waves_standing_air-001.png

Closed pipe

waves_standing_air-002.pngwaves_standing_air-003.pngwaves_standing_air-004.pngwaves_standing_air-005.png

Half-open pipe

waves_standing_air-006.pngwaves_standing_air-007.pngwaves_standing_air-008.pngwaves_standing_air-009.png

Open pipe

waves_standing_air-010.pngwaves_standing_air-011.pngwaves_standing_air-012.pngwaves_standing_air-013.png

Edit and compile if you like:

% Author: Izaak Neutelings (December 2020)
% http://hyperphysics.phy-astr.gsu.edu/hbase/Waves/standw.html
\documentclass[border=3pt,tikz]{standalone}
\usepackage{amsmath}
\usepackage{etoolbox} % ifthen
\usepackage{tikz}
\usetikzlibrary{arrows.meta} % for arrow size
\tikzset{>=latex} % for LaTeX arrow head
\colorlet{xcol}{blue!70!black}
\colorlet{vcol}{green!60!black}
\colorlet{Pcol}{orange!80!black}
\colorlet{dense air}{Pcol!70!red!60}
\colorlet{thin air}{brown!10}
\colorlet{myred}{red!65!black}
\tikzstyle{vvec}=[->,vcol,very thick,line cap=round]
\tikzstyle{wood}=[very thick,brown!70!black]
\tikzstyle{Pline}=[Pcol,very thick,line cap=round]
\def\tick#1#2{\draw[thick] (#1) ++ (#2:0.1) --++ (#2-180:0.2)}
\tikzstyle{myarr}=[xcol!50,-{Latex[length=3,width=2]}]
\begin{document}
% STANDING WAVE
\begin{tikzpicture}
\message{Standing wave plot...^^J}
\def\lam{2.0} % wavelength
\def\n{2} % harmonic
\def\L{\n*\lam} % length
\def\ymax{0.85} % y maximum
\def\xmax{1.02*\L} % x maximum
\def\A{0.80*\ymax} % amplitude
\def\D{1.20*\ymax} % pipe diameter
\def\s{2.45*\ymax} % shift
\def\N{1200} % number of points
%\def\N{500} % number of points
% DISPLACEMENT
\foreach \i [evaluate={\x=(\i-0.75)*\lam;}] in {1,...,\n}{
\draw[myarr] (\x,0.15*\A) --++ (0,0.65*\A);
\draw[myarr] (\x+\lam/2,-0.15*\A) --++ (0,-0.65*\A);
 
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Click to download: waves_standing_air.texwaves_standing_air.pdf
Open in Overleaf: waves_standing_air.tex

2 Replies to “Standing waves in air”

  1. Hello Izaak,

    Let me ask you something (not tikz related), in the first diagram of this series, I see that the arrows on the “tubes” t=0 and t = T/2 are always pointing from low to high pressure. Could explain why that is?

    I just thought that pointing from high to low pressure would be the “correct” way.

    Thank you,

    Wagner.

    1. Hi Wagner,

      It is to indicate movement, or equivalently, the displacement (s) of air molecules which is 90° out of phase with pressure differences (ΔP), which is why I used blue arrows, like the blue graph of s vs. time. I guess it could be made more explicit and clear by indicating an “s” above the arrows.

      Izaak

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