Transverse and longitudinal waves
Determination of
frequency and wavelength
Stationary waves
Description
In this Open/Closed Pipe wave model, lets consider a narrow pipe along the
OX axis. The simulation will display the first 5 normal modes, which are
From
the drop-down menu, the mode n = 1, ...,5, may be selected.
Units are
arbitrary set to be in SI unit for calculation purposes
The
modeling equation is governed by u(t,x) where
-
u(t,x) = A sin(n π x) cos(ω t +
δ) when both ends are closed.
-
u(t,x) = A sin((n-1/2) π x)
cos(ω t + δ) when the left end is closed and the right end open.
-
u(t,x) = A cos((n-1/2) π x)
cos(ω t + δ) when the left end is open and the right end closed.
-
u(t,x) = A cos(n π x) cos(ω t +
δ) when both ends are open.
Play with the Model. Test what you've learned by exploring the amplitudes,
wavelengths, periods, frequencies and wave velocities.
Sample Learning Goals
(a) show an understanding and use the terms displacement, amplitude, phase
difference, period,
frequency, wavelength and speed
(b) deduce, from
the definitions of speed, frequency and wavelength, the equation v = fλ
(c)
recall and use the equation v = fλ
(f) analyse and interpret
graphical representations of transverse and longitudinal
waves
(i) determine the wavelength of sound using stationary waves.
(a)
explain and use the principle of superposition in simple applications
(b)
show an understanding of experiments which demonstrate stationary waves
using microwaves, stretched strings and air columns
(c) explain the
formation of a stationary wave using a graphical method, and identify
nodes and antinodes
Activities
-
Compute the position of the nodes(always zero displacement) for mode
number n=1,2,3,4,5 cases for an open-open end system of the air in the
pipe.
-
Use the simulation to check your calculation.
-
select the correct modeling equation for fixed end string n=1,2,3,4,5
respectively.
-
how can you suggest is the parameter that describe these series of
stationary waves.
Version:
-
http://weelookang.blogspot.sg/2015/08/ejss-standing-wave-in-pipe-model.html
-
http://weelookang.blogspot.sg/2015/07/ejss-standing-wave-in-pipe-model.html
-
http://iwant2study.org/lookangejss/04waves_12generalwaves/ejs/ejs_model_pipewee02.jar
-
http://iwant2study.org/lookangejss/04waves_12generalwaves/ejs/ejs_model_pipestringwee01.jar
-