About

Topics

Progressive waves
Transverse and longitudinal waves
Determination of frequency and wavelength
Stationary waves

Description

In this Wave representations simulation, you have two representations of wave motion to work with. The left one shows a movie of the wave traveling along a string - you can think of this representation as a sequence of photographs. The second right representation is a plot of the displacement as a function of time for two points on the string (you can select which two points to use). Using only these two representations, you can determine the values of many different parameters that describe the wave by changing the slider values or input fields. Hints have also been designed in for ease of visualizing the meaning of these parameters.

Play with the Wave Representations Model. Test what you've learned by exploring the amplitudes, wavelengths, periods, angular frequency, frequencies,  wave velocities, maximum transverse velocity (linking to simple harmonic motion) and phase difference.

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
(c) SHM: understand and use the terms amplitude, period, frequency, angular frequency and phase difference and express the period in terms of both frequency and angular frequency

Activities

Reset the simulation to get a new random wave you are happy with.
Amplitude, A and wavelength, λ  can be determined using the left graph of displacement versus position.
Then, play the simulation until you have a nice position versus time graph. Period, T and angular frequency, ω and frequency, f and phase difference between x1 and x2,  φ using the relationship φ/(2π) = t/T, where t is the time difference between x1 and x2, can be determined using the right graph of displacement of x1 and x2 versus time.

Using both graphs, it is possible to determine wave velocity v = f λ, maximum transverse speed of a single point on the string, vmax=  A ω. You can check your answers as many times as you want. The amplitude. The wavelength. The period. The angular frequency. The wave speed. The maximum transverse speed of a single point on the string.

Version:

1. http://weelookang.blogspot.sg/2015/08/ejss-wave-representation-model.html
2. http://weelookang.blogspot.sg/2011/04/ejs-open-source-wave-representations.html
3. http://iwant2study.org/lookangejss/04waves_12generalwaves/ejs/ejs_model_Wave_representations_v5.jar
4. 
   

http://weelookang.blogspot.sg/2015/08/ejss-wave-representation-model.html

Wave representations

In this simulation, you have two representations of wave motion to work with. One shows a movie of the wave traveling along a string - you can think of this representation as a sequence of photographs. The second representation is a plot of the displacement as a function of time for two points on the string (you can select which two points to use). Using only these two representations, you can determine the values of many different parameters that describe the wave.

For more info : http://weelookang.blogspot.sg/2011/04/ejs-open-source-wave-representations.html

Activities

Keep pressing the "Get a new wave" button until you have a wave you are happy with. Then, play the simulation until you have a nice position versus time graph. Then, pause the simulation so that you have a photograph of the string as well as your position vs. time graph to work with. For each parameter below, figure out which of the two representations you need to determine the value of the parameter, and then find the value. You can check your answers as many times as you want.

1. The amplitude.
2. The wavelength.
3. The period.
4. The angular frequency.
5. The wave speed.
6. The maximum transverse speed of a single point on the string.

 

Translations

Code	Language		Translator	Run

Credits

Andrew Duffy; lookang; tina

http://iwant2study.org/lookangejss/04waves_12generalwaves/ejss_model_Wave_representations_v5/Wave_representations_v5_Simulation.xhtml

 Apps

https://play.google.com/store/apps/details?id=com.ionicframework.waverepresentation&rdid=com.ionicframework.waverepresentation 

Description

Introduction
Wave is an oscillation accompanied by a transfer of energy that travels through medium (space or mass)
Waves consist, instead, of oscillations or vibrations (of a physical quantity), around almost fixed locations
This simulation is on transverse wave where disturbance creates oscillations that are perpendicular to the propagation of energy transfer.
The equation for wave is A sin ( wt +kx + ϕ)
where 
A is the maximum amplitude of the wave, maximum distance from the highest point of the disturbance in the medium (the crest) to the equilibrium point during one wave cycle.
w is is the angular frequency
t is time
k is is the wavenumber
x is the position
ϕ is the is the phase constant

concepts illustrated in the simulations include
T is the time for one complete cycle of an oscillation of a wave
f is the number of periods per unit time (per second) and is related by T = 1/f
λ is the wavelength
v is the velocity of the wave travelling and is related by v= f λ
vtmax is the maximum transverse velocity of the wave particle that occurs at the displacement d =0.

 

Examples

EJSS wave representation model

Equation used to model the wave is \( y = A sin ( \omega t  - k x )  \)

Amplitude A

amplitude of wave = 0.18 m, maximum displacement from equilibrium position https://sg.iwant2study.org/ospsg/index.php/112 Direct Link

amplitude of wave = 0.20 m, maximum displacement from equilibrium position http://weelookang.blogspot.sg/2015/08/ejss-wave-representation-model.html run: Link1, Link2 download: Link1, source: Link1, Link2 author: Andrew Duffy, lookang, tina author EJS: Francisco Esquembre

wavelength λ

wavelength of wave = 1.70 m The wavelength λ  wavelength is the distance between two sequential crests or troughs (or other equivalent points) https://sg.iwant2study.org/ospsg/index.php/112 Direct Link

wavelength of wave = 0.50 m The wavelength λ  wavelength is the distance between two sequential crests or troughs (or other equivalent points) http://weelookang.blogspot.sg/2015/08/ejss-wave-representation-model.html run: Link1, Link2 download: Link1, Link2 source: Link1, Link2 author: Andrew Duffy, lookang, tina author EJS: Francisco Esquembre

Period T

period of wave = 3.00 s, The period T is the time for one complete cycle of an oscillation of a wave https://sg.iwant2study.org/ospsg/index.php/112 Direct Link

period of wave = 3.00 s, The period T is the time for one complete cycle of an oscillation of a wave http://weelookang.blogspot.sg/2015/08/ejss-wave-representation-model.html run: Link1, Link2 download: Link1, Link2 source: Link1, Link2 author: Andrew Duffy, lookang, tina author EJS: Francisco Esquembre

angular frequency f

The frequency f = 1/T  is the number of periods per unit time (per second) and is typically measured in hertz https://sg.iwant2study.org/ospsg/index.php/112 Direct Link

The frequency f = 1/T is the number of periods per unit time (per second) and is typically measured in hertz http://weelookang.blogspot.sg/2015/08/ejss-wave-representation-model.html run: Link1, Link2 download: Link1, Link2 source: Link1, Link2 author: Andrew Duffy, lookang, tina author EJS: Francisco Esquembre

 

angular velocity of wave ω

angular frequencyω  = 2.09 s, The angular frequencyω represents the frequency in radians per second. https://sg.iwant2study.org/ospsg/index.php/112 Direct Link

angular frequencyω  = 2.09 s, The angular frequencyω represents the frequency in radians per second. http://weelookang.blogspot.sg/2015/08/ejss-wave-representation-model.html run: Link1, Link2 download: Link1, Link2 source: Link1, Link2 author: Andrew Duffy, lookang, tina author EJS: Francisco Esquembre

phase difference ϕ

the phase of a vibration (that is, its position within the vibration cycle) ϕ measured in radians taking ratio "ϕ/(2π)= Δt/T",  ϕ = 2π(2.5-0.75)/3 =3.7 rad approximately https://sg.iwant2study.org/ospsg/index.php/112 Direct Link

 

wave speed v

sinusoidal waveform traveling at constant speed v is given by v = f λ https://sg.iwant2study.org/ospsg/index.php/112 Direct Link

sinusoidal waveform traveling at constant speed v is given by v = f λ http://weelookang.blogspot.sg/2015/08/ejss-wave-representation-model.html run: Link1, Link2 download: Link1, Link2 source: Link1, Link2 author: Andrew Duffy, lookang, tina author EJS: Francisco Esquembre

maximum transverse speed vmax

The maximum transverse velocity is vmax = Aω and it occurs when the particle on the wave travels passes through the equilibrium position https://sg.iwant2study.org/ospsg/index.php/112 Direct Link

The maximum transverse velocity is vmax = Aω and it occurs when the particle on the wave travels passes through the equilibrium position http://weelookang.blogspot.sg/2015/08/ejss-wave-representation-model.html run: Link1, Link2 download: Link1, Link2 source: Link1, Link2 author: Andrew Duffy, lookang, tina author EJS: Francisco Esquembre

 

reference:

http://weelookang.blogspot.sg/2011/04/ejs-open-source-wave-representations.html

Video

 

 

Versions

1. http://weelookang.blogspot.sg/2015/08/ejss-wave-representation-model.html Blog post of JavaScript version of Wave Representations by Andrew Duffy and Loo Kang Wee
2. http://weelookang.blogspot.sg/2011/04/ejs-open-source-wave-representations.html Blog post of Java version of Wave Representations by Andrew Duffy and Loo Kang Wee
3. http://iwant2study.org/lookangejss/04waves_12generalwaves/ejs/ejs_model_Wave_representations_v5.jar Java version of Wave Representations by Andrew Duffy and Loo Kang Wee

Other Resources

1. http://physics.bu.edu/~duffy/HTML5/wave_movie_and_graph.htmlby Andrew Duffy
2. http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=2405.0 One dimensional moving wave y(x,t)=A sin(k*x-w*t) by  Fu-Kwun Hwang

 

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