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Transverse waves
In this activity you will use Desmos to contruct a travelling transverse wave.
You can find Desmos here. Click on Create Account and use your school email address to sign-in.
Click on Untitled Graph
And type in a suitable title e.g. Transverse Waves and click Save.
Constructing a point with SHM
Click on Add Item and choose Image. You will want a PNG image. Search for an object online with png added to your search results (e.g. Google - trump png) Select an image from your pictures folder e.g. a small green ball!
Adjust the size of the ball using the corner points.
The formula for the displacement of a particle undergoing SHM is:
where A is amplitude
ω is angular frequency (ω= 2πf)
and t is time.
Click on the y coordinate of the (x,y) coordinates of the green ball and type in the equation above.
Then click on ALL so that sliders appear for the variables in the equation A, w and t.
Click on the parameter numbers on the time t slider and set the parameters to e.g. 0 < t < 100 step: 0.1
Click on Play on the time t slider and then click on the forward/reverse symbol as shown below and set it to the forward/forward symbol.
The object should now be oscillating with SHM.
Now investigate the effect of changing the amplitude A and the angular frequency w sliders.
Adding a phase difference
A wave is made up of a lot of points each oscillating out of phase with the others, the phase Φ is related to the position, x along the wave by the equation
where:
λ is the wavelength of the wave.
So the complete equation is
Click on Add Item and choose Expression:
Type in the complete equation into the space.
Click on the k button to add a slider for the constant k.
A sinusoidal wave should now appear as shown.
Now press the Play button on the time slider and observe the motion of the wave and the green ball.
The definition of a transverse wave is that the particles that make up the wave oscillate at RIGHT ANGLES to the direction of propagation of the wave energy.
Investigate the effect of changing the wave constant k.
Now investigate the effect of changing the sign in the complete equation to
Superposition of two waves
Now investigate the effect of two waves travelling in opposite directions.
Set the equation of the original expression y as f(x)
then add an additional Expression g(x)
Then add a further Expression h(x) that will sum the displacements of the two waves.
Click on the Play button on the time slider again and observe the combination of the two transverse waves over time.
Superposition of waves - the resultant displacement at any point in time is the sum of the individual wave displacements.
If everything has gone correctly your Desmos should look something like the page below: (Please note that I have changed the variable k in g(x) to the variable q, to allow for waves of different frequencies.
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