| Object diameter and ripple wavelength |
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Wirathip Thanapisitikul (Win): 2004
Research question
Is there a relation between the dimensions of an object and the wavelength of the ripples that are created when the object is dropped into still water?
Hypothesis
If the release height of the objects is kept constant, the initial
Potential Energy is dependent solely on the mass. More PE means
more KE on impact add more force during the collision. This in
turn will cause a longer wavelength of the ripples created after
the impact. Additionally, large objects will have a larger area
of impact on the surface of the water. This in turn will increase
the wavelength of the ripples.
Procedure
In order to measure the ripple wavelength when an object is
dropped on to a still
water surface (a pool), a digital camera is used to capture a
still photograph. A variety of objects were selected for this
experiment.
To prove the first part of the hypothesis, we must establish whether
there is a relationship between the mass of an object and the
wavelength.
A hole was cut into a hollow rubber ball so that one-kilogram
of sand could be poured into it. The ball was then dropped on
to the surface of the still water and a picture of the ripples
was captured. The next step was to add half a kilogram and
again photograph the ripples.
The diameter of the ball was measured. Using a graphic editing
program, red ellipses were drawn to outline each ripple. The wavelength
could then be measured by using the diameter of the ball as a
scale of measurement. This step was repeated for all pictures
taken for all different objects.
To find if there is a relationship between the object's size and the ripple wavelength, objects with different sizes and shapes were dropped into the pool. Photographs were taken for each object.
Data: different masses
1.0 kg and 1.5 kg
Data: different sizes
Diameter = 5 cm Wavelength = 5.5 cm
Diameter = 15.5 cm Wavelength = 16 cm
Diameter = 14 cm Wavelength = 13.9 cm
Table 1
Object diameter and ripple wavelength
The figure 2a shows the result when a 1.0 kg ball was dropped into the pond. The lower figure (2b) shows the effect of the same ball with a mass of 1.5 kg. Since the ripples have identical wavelengths, the mass of the ball is seen to have no effect.
Plotting the data in Table 1 gives a straight line graph with a slope of 1.0 within errors of ±10%. The ripple wavelength is equal (within errors)to the diameter of the object. There is a one-to-one relationship between object size and ripple wavelength. The ripples in all cases appear to be circular.
A cube that is 2 cm on each side is dropped with one face flat
into the water. The center of each edge is 1 cm from the
center of the square, but a corner is 1.414 cm from the center.
The ripple wavelength is comparable to the size of the object.
The velocity of waves in water is isotropic (the same in all directions),
so when the wave has traveled 10 cm outward, an initially square
wave would be 11.0 cm from the center of the square along the
directions of the edge centers, and 11.4 cm from the center of
the square along the directions of the corners. The further
the waves travel from the object, the closer the waves become
to accurate circles. This applies to waves expanding from the
crater made by any irregular shape.
Evaluation
The hypothesis was partially correct; the ripple wavelength is
proportional to the size of the object. but there is no increase
in wavelength with increasing mass.
There are many errors in measurement. The shape of the object
when it collides with the water surface depends on its orientation.
Since the images were taken from an angle the ripple images are
ellipses and using the diameter as a scale will not always give
an accurate reading of the actual wavelength. A bird's eye view
would improve the accuracy of the measurements. Despite these
limitations, there is an obvious relation between object size
and ripple wavelength.
Suggestions for improvements:
1 A camera could be mounted directly above the water surface. Because the time interval between the ball colliding with the water surface and the creation of the ripples is extremely short, a digital video camera could be used to capture the entire process. The video could then be uploaded to a computer and converted to a single frame image file.
2 A large meter stick could be placed on the bottom of the pond to be used as a scale, instead of the object itself.
Questions:
1 Does the force of impact affect the wave length of the object (change the height in which the object is being dropped)? I don't think it will because even when the mass changes, the wavelength remains the same. Therefore PE does not affect the wavelength.
2 Does the surface tension of the liquid (e.g. water, gasoline, alcohol) affect the ripple wavelength?
3 What part does the initial crater play in the formation of circular ripples?
Suggestions for further work:
Editors note:
This work is preliminary, exploring an original idea. The effect is well worth further study. Photographs would be better obtained from a video clip and they could be corrected for perspective in Adobe. The explanation offered for the circular nature of the ripples requires more thought. The crater blasted by an object on initial impact appears to be more circular than the object. Waves propagate from the crater rim both inwards to form a peak and outwards to form the expanding ripples.