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The Effects of Depth on Speed of Waves in Water

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The Effects of Depth on Speed of Waves in Water

The aim of this experiment is to investigate the relationship between
the depth of water and the speed of the wave in it. By studying the
speed of a single wave in the water as it travels along a tray it is
possible to find how the depth of the water affects the speed of the
wave. I will generate the pulse in the tray of water by dropping the
tray from a height of 5cm.



Background Knowledge
====================

A wave is a continuous movement of individual particles to form a way
of transportation of water, light, sound and others such as
paraphernalia. There are two different types of waves shown below.

Transverse waves are waves that cause a crosswise disturbance of the
medium through which they travel.

[IMAGE]

Longitudinal waves are waves that have vibrations travelling in the
same direction as the wave itself.

[IMAGE]

In my experiment I will be studying transverse waves. The speed of the
wave may be calculated by timing the motion of the wave from one end
of the tray to the other. A measurement of how far the wave travelled
as it move backwards and forwards will be needed.

I will use the following equation to work out the speed of the wave:

[IMAGE]


Hypothesis
----------

I predict that the greater the depth of water, the faster the waves
will travel. The reason for this is that when the water is shallow,
the container bottom begins to interfere with water motion. The bottom
constrains the water motion and results in a dragging affect on the
waves. Also, the deeper the water the greater the mass and therefore
force of the wave, which creates more momentum and speed.

I also predict that my graph will be a curve. I predicted that the
greater the depth the faster the wave will travel, however at a
certain depth the wave will reach an optimum speed that it will not be
able to exceed hence the graph will be in the shape of a curve. The
reason that the speed of the wave will reach an optimum is because the
water will come to a depth where there is enough water for it not to
interact with the bottom of the tray and there will then be no reason
for the speed to increase. Below is a graph to show how I think my
results will be illustrated on a graph.

[IMAGE]


Variables

As always, there are variables that can affect our results. I will
have to keep changing one of the variables hence its name: the
independent variable. All the other variables will have to be kept
constant. These include the length of the tray, the surface area of
the tray, the viscosity of the liquid, the height from which the tray
is dropped, the amount of times the wave goes backwards and forwards.

The independent variable in this experiment will be the depth of the
water. I found out that 1200ml would give a depth of 1cm and so I
decided that I would increase the depth by 500ml increasing the depth
by 0.4cm each time. I hope to get at least five readings so that I can
makes some suitable conclusions to my investigation.

My dependent variable will obviously be the speed of the wave. This is
because in this experiment I want to study the relationship between
depth and speed and the speed will only change as I change the depth.

The length and the surface area of the tray will also have to be kept
constant. Firstly, this means not changing the tray used with a new
one! To make sure that the surface area is the same for each
experiment I will take a measurement of the depth of the water five
times in each separate experiment. I will then take an average to make
sure that the surface area is constant. I will note this down to be
the depth. However, I have calculated that the average depths should
be as follows: 0cm, 0.4cm, 0.8cm etc. If it is not I will note down
the correct depth.

The viscosity of the liquid is an important variable. The less runny
the liquid the more slowly the particles will move up and down thus
the wave will become slower. In this experiment the same liquid will
be used for each separate experiment. This liquid will be water and
therefore it is not likely that the range of viscosity will be large
enough to significantly affect the velocity of the wave.

The height that I drop the tray must be kept constant, as a greater
height would mean a bigger force, which would mean that there would be
a bigger acceleration and speed. This is illustrated by the equation:

[IMAGE]

I have decided to drop the tray from a height of 5cm as it will make a
good starting push and will create a noticeable wave. It will also not
splash any water out of the tray!

Lastly, the amount of times that the waves move backwards and forwards
must be kept constant. This is because as the wave continues to
reflect itself the force acting upon the wave weakens and the speed of
the wave decreases. Thus if the wave is left to travel a very large
distance then the speed of the wave may not be constant, making my
results irrelevant. I decided that I would let the wav move back and
forth 3 times.


Risk Assessment and Precision

For precision I will have three readings for each particular
experiment and then find an average measurement, which will be plotted
on the graph and will be analysed.

I will vary the water depth at least five times with an increasing
interval of 0.4cm. If I have time to take more readings at other
depths I will but I have to makes sure that I have at least five so I
can make suitable conclusions.

I will also take my reaction time, so any anomalous data can be
explained. I will take my reaction time by starting the stopwatch and
then immediately stopping it as fast as I can. I will do this three
times and then find an average for my reaction time. I will do this to
make sure my reaction time is accurate.

There is only one safety measure to take in this experiment, as we are
not dealing with dangerous objects such as glass or acidic chemicals!
This safety precaution is if by accident there is a water spillage, a
“slip hazard”, one should immediately get some tissues and mop it up
until it is safe to carry on with the experiment.


Apparatus

Below is a list of apparatus that will be needed to carry out the
experiment:

F A plastic tray

F A small ruler (measuring centimetres)

F A metre ruler (measuring in millimetres)

F A beaker (measuring 500ml)

F A stopwatch

F A piece of paper (with a table to write down your results)

F A pen

1. The plastic tray will be used as a container for the water.

2. A small ruler will be used to measure the height at which the tray
will be dropped (in our case it will be 5cm)

3. A metre ruler to measure the depth of the water and to make sure
the surface area is equal.

4. A beaker will be used to add 500ml to the tray to increase the
depth by 0.4cm.

5. A stopwatch will be used as an instrument to time the speed of the
wave.

6. A piece of paper and pen will be used to record the results.


Method

1. Set up all the apparatus on the laboratory bench. Make sure that
you have a piece of paper (with a table to record your results)
and a pen.

2. Fill the beaker with 500ml and empty this into the tray.

3. With the metre ruler at five different places in the tray measure
the depth and find an average. This should be approximately 0.4cm
for every 500ml.

4. Write down this average depth in the depth column on your results
table.

5. Now measure the length of the tray with the metre ruler. Multiply
this by three and write down the value under the distance column.

6. Measure your reaction time using the stopwatch by quickly
starting and stopping the stopwatch. As said before do this three
times and then find an average, making this you reaction time.

7. By now the water in the tray must be relatively still. Measure
with your small ruler 5cm upright.

8. Lift the tray to the 5cm height you have measured with the ruler.

9. Again wait for the water in the tray to become moderately still.

10. Now drop the tray and start the stopwatch as it hits the surface
of the laboratory bench.

11. Watch the wave move backwards and forwards three times and stop
the stopwatch as soon as it hits one of the ends for the third
time.

12. Record the result and repeat the experiment three times for each
depth.

13. Below is a table for each of the other depths.

Depth of water (cm)

Volume of water to add to the tray each time (ml)

0.0

0

0.4

600

0.8

600

1.2

600

1.6

600



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"The Effects of Depth on Speed of Waves in Water." 123HelpMe.com. 18 Apr 2014
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