# 0.4 Transverse waves  (Page 5/10)

 Page 5 / 10

## Graphs of particle motion (not in caps - included for interest)

In Transverse Pulses , we saw that when a pulse moves through a medium, there are two different motions: the motion of the particles of the medium and the motion of the pulse. These two motions are at right angles to each other when the pulse is transverse. Since a transverse wave is a series of transverse pulses, the particle in the medium and the wave move in exactly the same way as for the pulse.

When a transverse wave moves horizontally through the medium, the particles in the medium only move up and down. We can see this in the figure below, which shows the motion of a single particle as a transverse wave moves through the medium.

A particle in the medium only moves up and down when a transverse wave moves horizontally through the medium.

As in Transverse Pulses , we can draw a graph of the particles' position as a function of time. For the wave shown in the above figure, we can draw the graph shown below.

The graph of the particle's velocity as a function of time is obtained by taking the gradient of the position vs. time graph. The graph of velocity vs. time for the position vs. time graph above, is shown in the graph below.

The graph of the particle's acceleration as a function of time is obtained by taking the gradient of the velocity vs. time graph. The graph of acceleration vs. time for the position vs. time graph shown above, is shown below.

As for motion in one dimension, these graphs can be used to describe the motion of the particle in the medium. This is illustrated in the worked examples below.

The following graph shows the position of a particle of a wave as a function of time.

1. Draw the corresponding velocity vs. time graph for the particle.
2. Draw the corresponding acceleration vs. time graph for the particle.
1. The $y$ vs. $t$ graph is given. The ${v}_{y}$ vs. $t$ and ${a}_{y}$ vs. $t$ graphs are required.
2. To find the velocity of the particle we need to find the gradient of the $y$ vs. $t$ graph at each time. At point A the gradient is a maximum and positive.At point B the gradient is zero. At point C the gradient is a maximum, but negative.At point D the gradient is zero. At point E the gradient is a maximum and positive again.
3. To find the acceleration of the particle we need to find the gradient of the ${v}_{y}$ vs. $t$ graph at each time. At point A the gradient is zero.At point B the gradient is negative and a maximum. At point C the gradient is zero.At point D the gradient is positive and a maximum. At point E the gradient is zero.

## Mathematical description of waves

If you look carefully at the pictures of waves you will notice that they look very much like sine or cosine functions. This is correct. Waves can be described by trigonometric functions that are functions of time or of position.Depending on which case we are dealing with the function will be a function of $t$ or $x$ . For example, a function of position would be:

$y\left(x\right)=Asin\left({360}^{\circ },\frac{x}{\lambda },+,\phi \right)$

#### Questions & Answers

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SUYASH
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Ebrahim
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Ebrahim
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s.
Graphene has a hexagonal structure
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Cied
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Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
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Source:  OpenStax, Physics - grade 10 [caps 2011]. OpenStax CNX. Jun 14, 2011 Download for free at http://cnx.org/content/col11298/1.3
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