Figure 2
- Repeat stages 1-4 using the following amounts of water
- Record all results and then average
To make sure this is a fair test I must consider all the possible variables in this experiment which can affect the speed of the wave in my experiment and control them. One main variable in the depth of the water which is what I am measuring to obtain my results and so this must be changed. In my practise experiments I found that the best depth to start at was 0.5cm (a volume of 600ml) because anything lower than this moved to slowly and wasn’t noticeable enough to record the times I also decided that the maximum depth of the water was 4cm because anything more than this and the wave’s amplitude was high enough to spill the water over the edge of the tray. Another variable is the surface area of the tray; this cannot change because even if the water is the same volume the depth of it will b different and because the depth of the water is a main variable in the investigation it must stay constant.
The viscosity of the liquid being used is also an important variable because the more viscous the liquid the less quickly and the less easily the particles will be able to move up and down so the speed of the wave will be slower. In my experiment the liquid I am using is water as so it is highly unlikely that range in viscosity of each tray full will be enough to affect the speed of the wave that greatly.
Two more important variables in this experiment are the height at which the tray is dropped and the amount of times you let the waves reflect back and forth. In both cases these variables must stay constant. The wave speed is likely to change according to the drop height of the tray because a tray dropped from a greater height will mean a greater force on the wave which according to the equation:
F = ma
(Patrick Fullick’s GCSE Physics)
will give the wave a greater acceleration and speed. This variable can be kept the same by always dropping the tray from the same height as shown in fig 1. In my practise experiments I decide on the height of my ruler when put on its side as a dropping height because firstly in was the only object I had available that would give a constant dropping height and also the height of the ruler gave a good starting force which was enough to begin a wave but not to spill or create an unnoticeable wave.
The amount of times that I time the wave going back and forth must also stay constant because as the wave continues to reflect itself the weaker the force on the wave and the slower the speed will become and therefore if the wave is left to travel too much then the velocity of it will not be constant and therefore the results will not be accurate. In my practise experiment I observed how many times it takes for the wave to slow down noticeably and came to the conclusion that letting it go back and forth 3 times is the best amount.
Prediction:
Larger waves in very deep water can be described in this equation
(Akrill, Bennet and Millar’s Physics Second Addition)
where c is the velocity of the wave, g is the gravitational acceleration (constant) and is the wavelength.
However, in my experiment I am dealing with much smaller waves and much shallower waters so they will be tested by a different equation which is
Where v is the speed of the water and h is the depth.
This equation basically shows that the speed of the wave will increase as the depth of the water increases. This is because in shallow water the waves on the surface are bigger than the depth of the water and so they hit the bottom of the tray and so it cannot travel properly. As the wave hits the bottom of the tray it looses energy, mainly through friction and so the shallower the water the most energy is lost, the more friction is created and therefore the slower the wave travels.
If you notice, the equation is not linear which means that at some point the velocity of the wave will peak because the water will come to a depth that is amply enough for it not to touch the bottom and so there is no need for the speed to increase anymore.
Results:
Above is a table and graph of the data I collected
Data Analysis:
The data I collected shows a clear relationship between the depth of the water and the velocity of the wave but it also proves that my prediction that the velocity of a wave will increase as the depth of the water increases. There were no anomalies but the data is not one hundred percent exact it still shows clearly the relationship between the two.
Conclusion:
The results I recorded show with accuracy that my prediction was correct and that according to the equation
It shows that the velocity of the wave increase as the depth of the water does. The reason for this is that in very shallow water the wave will frequently hit the bottom and in doing this will loose some of its energy (mainly due to friction) and as a result its velocity will be slower. As the depth of the water increases the wave hits the bottom less frequently and therefore looses less kinetic energy, this is the energy that it propelling it and so it travels faster than that of a wave in shallower water. Although in my graph it shows this theory, however true it is to that data, in actually fact the velocity of a wave does not continue to increase with the depth of the water after a certain point because after a certain depth the water actually stops hitting the bottom of the container altogether and so no energy is being lost and neither is it being gained so however much more liquid you put in from there the velocity of the wave will still remain the same.
Through the equation
And the explanation above I can also conclude that the velocity and depth are in direct proportion to each other
Evaluation:
In my opinion my experiment was successful. It show the relationship between velocity and depth well and also help to prove my predictions but it is also true that my result were not completely exact and these could be due to a couple of things. One of them is that it was very hard to start with the exact same starting force each time because the speed at which I removed the ruler from beneath the tray of water would not have been completely constant. To have improved this is would have helped if I had measure the angle of elevation as well as the height of it because this would have help keep the starting force more accurate. Another thing that could have affected the end results was the accuracy of the timing as it was quite difficult to stop and start the stop clock at the exact times that waves began and hit the side of the tray for the third time. Unfortunately there is no easy solution to this and the only thing that really could be done in order to make the results more accurate would be to record more tests and so the average would be closer to the actually time.
