Question:

How does the depth of a pool affect the speed and duration of the wavefront, regarding how it will impact a swimmers speed?

Introduction:

Turbulence is one of the biggest factors when it comes to competitive swimming, it has influenced the design of swimming pools and lane ropes for decades. Every stroke and kick a swimmer takes, they create turbulence in the form of waves. This is due to the large volumes of water the swimmer shoves behind them to move forward. This phenomenon is known as Newtons third law, as every action has an equal or opposite reaction. When a swimmer pulls on the water with their hands to move forward, they travel in the opposite direction of the palm pushing the water back. Being a national swimmer myself, I encounter all sorts of waves coming all different directions when I train. This becomes a hassle in the warm up pool were it becomes packed with swimmers creating waves, leaving the water to be very choppy, making it feel I’m swimming in open water (ocean). It has always fascinated me how the depth of a swimming pool can affect the speed of a swimmer. From a young age, swimmers learn in shallow pools due to their height. As they get older, they become too “big” for the shallow pools and progress to the deeper 50m pool. However, this is not the case for every pool, some pools had one half shallow, the other half slowing descending to a certain depth. I will explore how depth can affect the speed of a wave, I also will explore how it can affect the dissipation of a wave. It is ideal for a swimmer to have their wave dissipate as fast as possible whilst moving at the fastest possible rate. We do not want to be swimming into someone else’s wake as we need to exert more effort to overcome this, nor do we want to swim in our own.

Aim:

To determine how the depth of the water in a system can affect the wave speed and dissipation times.

Equipment:

  • Gift card, measuring (8.5cm x 12.4cm) as a wave generator.
  • Trough (long piece of guttering with both ends closed). Measuring (200cm x 5cm x 10cm).
  • One ruler the length of 15cm to measure the depth.
  • One ruler the length of 100cm to measure the length.
  • Stop watch
  • Jugs of water to fill up the guttering.
  • Polystyrene pieces 1cm by 1cm (cut up from a foam cup)

Safety/hazards:

Avoid getting any electrical equipment wet.

Clean up any spills of water to avoid slipping hazards.

Variables:

The independent variable for this experiment will be time for a given consistent distance.

The dependent variable for this experiment will be the depth of the water. I will change the depth of the water after each trial by filling it up with a jug.

I also need to control the creation of each wave, through the use of the gift card, to ensure I can get consistent precise results, which I will talk about more in-depth in my discussion.

Method:

  1. I first filled up the guttering with water to test for any leaks and to clean any debris.
  2. After I placed a ruler inside the trough to measure the height of the water and refilled the guttering with clean water to 0.65cm in depth.
  3. I ensured I removed the ruler before each trial so that it would not disturb the wave.
  4. I measured the air temperature as well as the water temperature.
  5. I place another ruler alongside the trough to measure the distance travelled by the wave front. This is vital in order to calculate the speed of the wave.
  6. I chose to time 1m in length so I marked the bottom of the guttering with pencil in 50cm increments to make up 1m.
  7. We did not have an appropriate wave generator so I used a large plastic card to create a wave.
  8. This meant that I needed to keep the generated wave as consistent as I could, I marked the bottom of the guttering to signify when to start and stop the wave (plastic card). This was 20cm in length.
  9. The wave had 15cm to travel before I started the stop watch in order to keep the wave consistent. As soon as the wavefront crossed the start line, I would immediately start the stopwatch, then I would follow the wavefront as best as I could to the finish line, stopping it straight after it crossed the finish line.
  10. I recorded 5 sets of data for every trial, between each trial I had to wait for the water to calm down otherwise I would encounter constructive and destructive waves.
  11. Once I recorded all the possible data, I went on to fill the trough higher by roughly 0.50 cm and repeated this process 6 more times.
  12. I had to bear in the mind, that the increased volume meant an increase in amplitude. When I reached by 7th trial, water started to spill over the edge of the guttering. Not only this, the great the volume, the longer I had to wait for it to dissipate.
  13. For the wave dissipation trials, I created a wave by using the method as stated above and left the wave to flow in the guttering. I placed little pieces of polystyrene onto the water as well as dust to help determine when the wave had completely dissipated. The polystyrene pieces are very light and move along with the wavefronts in the guttering, however once the wavefront stopped the polystyrene pieces would come to a rest. When this happened I stopped the stopwatch.
  14. I repeated step 13 for five trials and recorded in a table ready to be graphed.

Background information:

In an ideal scenario, water waves would not slow down and dissipate. However, waves in the real world slow down and dissipate due to various different factors such as turbulence, friction and obstructions. Friction is found at the bottom of the water as it covers the bottom of the pool/tank and this friction translates upwards, layer by layer. The deeper the water, the more layers the water will have to travel. Therefore the friction at the top will be lower compared to deeper water. This also means the shallow water would have more friction through the body of water as there are less layers. From background research on forums, I deduced that due to the friction occurring deeper in the water, the speed will be higher at the surface, however I will need to investigate this to see whether this theory reigns true.[1]

Results for Wavefront speed

Table of results for trial one

Table 1: raw data

Height/Depth of the water in D (cm)

Δ(D)=±0.01cm

Length that is timed.

L (cm)

Δ(L)=±0.01cm

Time take of the wavefront.

t (sec).

Δ(t)=±0.01s

Velocity of the wavefront.

V (m/s).

Δ(V)=±0.38m/s

Water temp = 21.0 oC

w (oC)

Δ(w)=±0.05oC

Air temp = 24.5 oC

a (oC)

Δ(a)=±0.05oC

0.65cm 100 2.87 0.348  
0.65cm 100 2.97 0.337  
0.65cm 100 3.10 0.323  
0.65cm 100 2.81 0.356  
0.65cm 100 2.72 0.368  
Average   2.89 0.346  

Table of results for trial two

Table 2: raw data

Height/Depth of the water in D (cm)

Δ(D)=±0.01cm

Length that is timed.

L (cm)

Δ(L)=±0.01cm

Time take of the wavefront.

t (sec).

Δ(t)=±0.01s

Velocity of the wavefront.

V (m/s).

Δ(V)=±0.41m/s

Water temp = 23.2 oC

w (oC)

Δ(w)=±0.05oC

Air temp = 24.5 oC

a (oC)

Δ(a)=±0.05oC

1.10cm 100 2.62 0.382  
1.10cm 100 2.56 0.390  
1.10cm 100 2.94 0.340  
1.10cm 100 2.62 0.382  
1.10cm 100 2.53 0.395  
Average   2.65 0.378  

Table of results for trial three

Table 3: raw data

Height/Depth of the water in D (cm)

Δ(D)=±0.01cm

Length that is timed.

L (cm)

Δ(L)=±0.01cm

Time take of the wavefront.

t (sec).

Δ(t)=±0.01s

Velocity of the wavefront.

V (m/s).

Δ(V)=±0.11m/s

Water temp = 21.7 oC

w (oC)

Δ(w)=±0.05oC

Air temp = 22.8 oC

a (oC)

Δ(a)=±0.05oC

1.95cm 100 1.90 0.526  
1.95cm 100 1.88 0.532  
1.95cm 100 1.85 0.541  
1.95cm 100 1.79 0.559  
1.95cm 100 1.81 0.552  
Average   1.85 0.541  

 

Table of results for trial four

Table 4: raw data

Height/Depth of the water in D (cm)

Δ(D)=±0.01cm

Length that is timed.

L (cm)

Δ(L)=±0.01cm

Time take of the wavefront.

t (sec).

Δ(t)=±0.01s

Velocity of the wavefront.

V (m/s).

Δ(V)=±0.12m/s

Water temp = 20.9 oC

w (oC)

Δ(w)=±0.05oC

Air temp = 22.3 oC

a (oC)

Δ(a)=±0.05oC

2.30cm 100 1.62 0.617  
2.30cm 100 1.53 0.654  
2.30cm 100 1.50 0.667  
2.30cm 100 1.56 0.641  
2.30cm 100 1.50 0.667  
Average   1.54 0.649  

Table of results for trial five

Table 5: raw data

Height/Depth of the water in D (cm)

Δ(D)=±0.01cm

Length that is timed.

L (cm)

Δ(L)=±0.01cm

Time take of the wavefront.

t (sec).

Δ(t)=±0.01s

Velocity of the wavefront.

V (m/s).

Δ(V)=±0.10m/s

Water temp = 20.5 oC

w (oC)

Δ(w)=±0.05oC

Air temp = 21.5 oC

a (oC)

Δ(a)=±0.05oC

2.85cm 100 1.44 0.694  
2.85cm 100 1.34 0.746  
2.85cm 100 1.38 0.725  
2.85cm 100 1.40 0.714  
2.85cm 100 1.43 0.699  
Average   1.40 0.714  

Table of results for trial six

Table 6: raw data

Height/Depth of the water in D (cm)

Δ(D)=±0.01cm

Length that is timed.

L (cm)

Δ(L)=±0.01cm

Time take of the wavefront.

t (sec).

Δ(t)=±0.01s

Velocity of the wavefront.

V (m/s).

Δ(V)=±0.06m/s

Water temp = 20.9 oC

w (oC)

Δ(w)=±0.05oC

Air temp = 22.3 oC

a (oC)

Δ(a)=±0.05oC

3.40cm 100 1.35 0.741  
3.40cm 100 1.34 0.746  
3.40cm 100 1.29 0.775  
3.40cm 100 1.29 0.775  
3.40cm 100 1.31 0.763  
Average   1.32 0.758  

Table of results for trial seven

Table 7: raw data

Height/Depth of the water in D (cm)

Δ(D)=±0.01cm

Length that is timed.

L (cm)

Δ(L)=±0.01cm

Time take of the wavefront.

t (sec).

Δ(t)=±0.01s

Velocity of the wavefront.

V (m/s).

Δ(V)=±0.04m/s

Water temp = 22.0 oC

w (oC)

Δ(w)=±0.05oC

Air temp = 23.8 oC

a (oC)

Δ(a)=±0.05oC

3.90cm 100 1.25 0.800  
3.90cm 100 1.21 0.826  
3.90cm 100 1.25 0.800  
3.90cm 100 1.25 0.800  
3.90cm 100 1.22 0.820  
Average   1.24 0.806  

Uncertainties

Calculation of uncertainty regarding the measurements

To get my length uncertainties on my ruler, which is an analogue instrument, I would use half the least measurable unit (cm).  This was ΔL = Δ± 0.05 cm, however I chose Δ± 0.1 cm instead, as I was looking as an awkward angle to find the water level, the larger uncertainty would be more suitable in this occasion as the surface tension of the water on the ruler was also another difficulty. I based all my measurements off the centre of the ruler which ended up being around the average of the water level.

Similar to the ruler, a thermometer is another analogue instrument. Therefore I deduced the uncertainty value of the thermometer to be Δtemperature = Δ±0.05oC.

For the stopwatch, the uncertainty would be Δt = Δ±0.01s, as the uncertainty for digital systems would be the last value that is recorded.

Calculation of uncertainty from maximum residual

The maximum residual was determined by finding the greatest difference between the mean of the data and the data itself. This value becomes the stated uncertainty.

To calculate the mean, I needed to add the five trials together, then I divided the sum of the trials by five.

I will use trial number one as an example:

Trial one

After I got my mean value for all the different heights, I then set out to find the maximum residual.

Going from trial one down to trial seven.

Our residuals are a great way of giving a numerical estimation of the variation due to random errors where our measurement errors are systematic.

Graph

From this graph taken from Excel, we can see a strong linear relationship however, we cannot say it’s directly proportional as it does not go through the origin. We get an equation of V=0.1522D + 0.2476, however the x axis is in cm whereas the y axis is in m. Once we change the x axis into m, we get the equation of V=15.22D +24.76.  As not all the error bars are touching the line of best fit, we can only assume that this is due to random errors that have not been added into the calculations. The error bars become too small to see on the graph towards the end. The systematic errors can only provide so much and the rest is due to the random errors. In this case, it would be mostly random errors. Despite having this problem, the relationship is still pretty clear and we can successfully deduce that the depth of a body of water has a relation to the speed of the wave.

Maximum Residual and Minimum residual lines

 

Table 8

Maximum slope D Maximum slope V Minimum slope D Minimum slope V
0.688 0.308 0.612 0.384
1.141 0.337 1.059 0.419
1.961 0.530 1.939 0.552
2.312 0.637 2.288 0.661
2.860 0.704 2.840 0.724
3.406 0.752 3.394 0.764
3.904 0.802 3.896 0.810

fsfgsdfg

The normal slope is in blue with the equation of V=0.1522D + 0.2476.

The maximum slope is in orange with the equation of V=0.1658D + 0.196.

The minimum slope is in grey with the equation of V=0.1389D + 0.2982.

Discussion of results:

From my graphed results, I can deduce that the deeper the water, the faster the surface wave will travel.

The equation of V=15.22D +24.76 shows that the rate of change regarding the depth of water to be 15s, as the two units of measurement cancel each other out. This could mean that the wave travels 15 seconds faster each m it is lowered. The linear growth would remain true for an ideal environment, however other factors will influence this gradient. The data going from the first data point to the y-intercept are all extrapolated data, meaning that they may not follow the linear trend of the other data points. This is further highlighted as I only a limited range to work with due to the height of the guttering’s walls.

What was important in doing my experiment was to keep everything consistent. Every time before I did a trial, I had to make sure that the water in the guttering was as calm as it could get. The easiest way to figure this out was to see if the dust particles in the water were moving or not, as the slightest wave movement can move the particles forwards and backwards. Not only this, reflection of light reflecting off the water surface allowed me to see whether or not the water was calm.

I also had to bear in mind that every time I created a wave, I had to make sure that this wave was consistent and moved the same percentage of volume regarding the volume and depth. I decided to set a distance to create the wave, it ended up being 15.0cm before I removed the card and let the wavefront go wild along the guttering. I had to do many trials to find the optimal length to build up the wave, which then I timed a 1m portion of the guttering.

What I noticed through observation was that the amplitude seemed to be lower when the depth was increased as well as the waves crashed back onto other wavefronts after they had collided with the edges of the guttering, which could slow down the waves due to drag and extra turbulence in the system.

I conducted the entire experiment with normal tap water, however there would a density difference when compared to a chlorinated pool. A chlorinated pool will be denser compared to tap water as there are more salts and other products in the pool water compared to your conventional tap water. Therefore there will an increase in buoyancy for the swimmer which helps the swimmer as floating easier in the pool means there is less energy required to stay afloat.

Not only this, I also measured the water temperature as well as the air temperature, this is because water temperature can affect the density. Similar to air, the warmer temperature water will rise and the cold temperature water will flow to the bottom. The waves are generated on the surface of the water so any difference of the water temperature would have a small effect on the wave, this could be one of the reasons for error in the prac, however unlikely in this system. In order to combat this for next time, we must ensure that we do this experiment in a controlled environment on the same day, not only this, when I add water to the guttering, I need to make sure that this would be the same temperature to keep my results consistent.

From all the data I have collated, I can interpret the following from my data:

Deeper water vs shallower water

Table 9: found data

  Deep Water Shallow Water
Friction Lower Higher
Velocity Higher Lower
Frequency Same Same
Wave length (v/f) Larger Smaller

 

Now all of these still kept me wondering and whilst I was swimming through the pool and watching other swimmers swim, I started to thinking about the dissipation of the wave. The wave doesn’t just stop automatically after the volume of water has been pushed, and I set to find out whether or not depth can influence the time it takes for a wave to full dissipate in the water.

Wave dissipation results

Here are the results from my second experiment. (Method step 13)

Table 10: raw data

  Height/Depth of the water in D (cm)

Δ(D)=±0.01cm

Water temp = 22.0 oC

w (oC)

Δ(w)=±0.05oC

Time for the wave to dissipate t (s)

Δ(t)=±0.01s

Trial one 1.10cm 23.5 1.06.25s
Trial two 1.10cm 23.5 1.09.00s
Trial three 1.10cm 23.5 1.07.78s
Average 1.10cm 23.5 1.07.68s ±2.75s

 

Table 11: raw data

  Height/Depth of the water in D (cm)

Δ(D)=±0.01cm

Water temp = 22.0 oC

w (oC)

Δ(w)=±0.05oC

Time for the wave to dissipate t (s)

Δ(t)=±0.01s

Trial one 1.80cm 23.5 1.21.87s
Trial two 1.80cm 23.5 1.23.88s
Trial three 1.80cm 23.5 1.21.38s
Average 1.80cm 23.5 1.22.38s ±2.50s

 

Table 12: raw data

  Height/Depth of the water in D (cm)

Δ(D)=±0.01cm

Water temp = 22.0 oC

w (oC)

Δ(w)=±0.05oC

Time for the wave to dissipate t (s)

Δ(t)=±0.01s

Trial one 2.05cm 23.7 1.41.37s
Trial two 2.05cm 23.7 1.38.82s
Trial three 2.05cm 23.7 1.35.18s
Average 2.05cm 23.7 1.38.46s ±6.19s

 

Table 13: raw data

  Height/Depth of the water in D (cm)

Δ(D)=±0.01cm

Water temp = 22.0 oC

w (oC)

Δ(w)=±0.05oC

Time for the wave to dissipate t (s)

Δ(t)=±0.01s

Trial one 2.50cm 23.0 1.41.50s
Trial two 2.50cm 23.0 1.45.43s
Trial three 2.50cm 23.0 1.43.19s
Average 2.50cm 23.0 1.43.38s ±3.93

 

Table 14: raw data

  Height/Depth of the water in D (cm)

Δ(D)=±0.01cm

Water temp = 22.0 oC

w (oC)

Δ(w)=±0.05oC

Time for the wave to dissipate t (s)

Δ(t)=±0.01s

Trial one 3.25cm 23.0 1.58.97s
Trial two 3.25cm 23.0 2.02.63s
Trial three 3.25cm 23.0 2.00.78s
Average 3.25cm 23.0 2.02.79s ±3.66

 

 

 

 

 

Wave dissipation graph

Following out previous steps, I worked out the residuals and error bars for the graphs.

Captureewqrwer

 

We can see a very strong linear relationship of t=28.81D+39.70 on the Dissipation of a wave graph. We can deduce that a change in depth will result in a change in the life of the wave. However the line doesn’t go through the origin. When you create a wave, it will still take some time to dissipate so this is rather accurate. The error bars are too small to be seen on the graph, however it is only the third point that does not touch the line of best fit.

Discussion part two

Sources of error

My greatest source of error came from the creation of the wave. I did my best to maintain the consistency of each wave. To ensure this, I had to discount any waves that did not come off right. This ensured that I would achieve precision. I had set markings on the bottom of the guttering to avoid this problem, however from the graphs, it can be seen that random errors were prominent. The depth of the how I placed the gift card was another source of error in this experiment and I ensured to place it at the same depth before each experiment, appropriate to the depth of the water. The wave reflecting off the wall can also be seen as an error as it slowed down the wavefront, it would be better next time to allow it to overflow so that the wavefront will not be affected by the rebounding waves. To combat the wave creation problem, dropping an object the width and height of the guttering to create a wave would be a better way, only if it can produce a recordable wave. Having a device like paddles like those ones on old steam boats or turbines could also be another way to create a wave that would stay constant throughout the trials.

The second greatest source of error came from the timing of the wave. It was all about perception of when the wavefront crossed the start line and crossed the finish line. As this was a solo prac, I had to create the wave with my left hand whilst holding the stopwatch with my right hand waiting for the wavefront to cross the finish line. One the button was pressed, I had to move hastily along the bench to ensure that I was over the wavefront when it crossed the finish line. This would fall under the parallax error as I was looking at the wavefront from an angle which would have caused some degree of an error. Not only this, my reaction time also come into play. As a swimmer, I react to the sound of the buzzer and I learn not to react from other things happening in the environment such as waves from the pool. Therefore it was harder for me to get an accurate timing. In order to combat this as best as I could, I had a few warmup attempts to get my head focused on the wave. To combat the parallax error, I would have to have a helper to create the wave which then I can focus on the wavefront. If I was to repeat this experiment, having a helper will dramatically improve this experiment. Setting up a camera to record the entirety of the wave would also dramatically improve the timing accuracy. Even better, two cameras in sync would provide the best results.

The third source of error came from the surrounding environment. This includes dust particles falling into the water overnight which could have some effect on the water. Not only this, the temperature of the water was greatly affected by the air temperature. Some days the air conditioner as on which led to the water being cooler meaning that it would be denser than the warmer water due to the kinetic energy of the molecules. When the water cools down, the molecules become more tightly packed and slow down, leaving them in a denser state. Since the guttering was placed on a table, any slight bumps or movement would create small waves or even whirlpools in the guttering. Someone walking past my experimental area also would create a wave on top of the calm water. One trial was being done during the end of school and people walking across the room or outside also had some effect. To combat this I would need to cover the guttering before leave for the day to ensure no particles would land in the water. It would best if this experiment was to be conducted in a controlled environment where the water temp and air temp remained constant to ensure that I can get the best possible results. Whilst in this controlled environment, walking and bumping into the table must be avoided to ensure that no waves are created prior to the trial.

Relation to a Swimmer

Olympic pools are designed to have a constant depth of 3m, this is because the swimming creates waves in all directions when they swim. The depth of 3m is required in order for the wave to dissipate in the water so it doesn’t reflect off the bottom back onto the swimmer. Not only this, the deeper the pool is, the less frictional drag the moving water will have against the bottom as not the entire body of water will move forward when a swimmer swims.

Costs also come into play when building a fast pool used for the Olympics, the deeper the pool, the higher the operating costs will be. Therefore they tend to cap the current Olympic pools to 3m, not only this, many of these pools have moveable floors to adjust the depth of the floor which is helpful when the pool is used for teaching and recreational swimming.

When I was doing my experiment I came across reflection of waves off the sides of the guttering and sometimes the amplitude of the wave was higher than the walls of the guttering which allowed it to overflow. This led me to ask question how to minimize the effects. After some research, I found that Olympic pools have specially designed lane ropes which are optimized to minimise the turbulent waves so Swimmers do not have to battle the waves coming from themselves, competitors or the walls.

The future of fast swimming pools will also be influenced by the future of walls, nowadays the touch pads do not absorb the waves and they get reflected back onto the swimmer when they turn, meaning that they need to escape this wavefront otherwise they will be pulled back by the wave. To combat this, some sort of wave absorbing material will need be implemented.

In 2014, controversy arose amongst the Glasgow commonwealth games as the competition swimming pool’s floor became stuck at a fixed height. It was supposed to be 2m in depth all the way, however during a certain length of the pool after 12m the pool arose to 1.88m. World championships and Olympic Games have a set ruling saying that the pool must be at least 2m in depth which caused a debate in the controversy of whether or not world records would be legitimate. However due to my prac results, a shallower depth pool would have made it harder for the swimmers to achieve world record times due to the increase in resistance. However, the governing body of swimming, FINA, approved any records that were set as the pool still exceeded their minimum requirements.

Conclusion

I must keep in mind of all possible errors for the next time I repeat this experiment. However, this time around, I managed to discover and answer my aim, which was to find and form a relationship and an equation to match the trend how the depth of the water affects the wave speed. V=15.22D +24.76 .This can all relate to how I swim, now I would much prefer to swim in the middle of the pool to avoid getting reflections off the side of the pool. Now in swimming I can pay attention to the effects on the swimmer from the changing depths. It is a common misconception that shallow pools are faster, my experiment has disproved this theory. Instead, it’s the deeper the pool, the faster the wave will travel at the surface. Hopefully soon there will be a solution to the wall problem where the wall will completely absorb the wave!

 

Referencing

Barret,C Luttion,P and Paxinos S. (2014). Officials insist records will stand despite defective pool floor. The Sydney Morning Herald. Retrieved 10 March 2016, from http://www.smh.com.au/commonwealth-games-glasgow-2014/commonwealth-games-news/officials-insist-records-will-stand-despite-defective-pool-floor-20140727-zxgyj.html

Sinclair, P. Why swimming records stand, even with a broken pool floor. (2014). The Conversation. Retrieved 10 March 2016, from http://theconversation.com/why-swimming-records-stand-even-with-a-broken-pool-floor-29834

 

[1]Based off findings on Quora. Why do waves in water slow down on entering shallower region? – Quora. (2016). [online] Quora.com. Available at: https://www.quora.com/Why-do-waves-in-water-slow-down-on-entering-shallower-region [Accessed 8 Mar. 2016].

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