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Initial Knowledge

A wave can be considered as an oscillation through the space-time fabric, passing through a medium, which is the space in which it passes by. The medium can be a substance, such as water or air, and in rare cases can pass through a vacuum (electromagnetic waves). Waves can vary in form (wavelength), velocity (wave speed) and frequency. A point on a wave never moves forward or backwards, but only oscillates on the y-axis.

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The Experiment

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Variables

Independent Variable	Water Depth	We have considered the values of 2 cm, 3 cm, 4 cm, 5 cm and 6cm for the depth of water in the tray. For each we have done three trials.
Dependent Variable	Wave Speed	We have focused on measuring the time [+/-0.01s] taken by a water wave to travel the length of the tray to one side and back [+/-0.1cm]. Wave speed is given by the ratio of the wavelength [+/-0.1cm] and the time taken for it to cover that distance [+/-0.01s].

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Controlled Variables

Dropping Height: 7cm

Water Tray

Type of Water
Water temperature
Wave to consider

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Hypothesis

What do you think will happen?
We suppose that when the amount of water is less the wave will be slower, and that higher the amount will faster it will go.
What do you think this will happen?
The waves will go slower when there is less water because they are more affected by friction with the tray, causing them to slow down. When instead there is more water the waves will be less affected by friction with the tray, increasing the wave speed.

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Procedure

Fill the container with tap water;
prepare the water tray on a flat and stable desk;
fix one ruler to the tray’s side, aligning its lower border with the 0 cm sign of the ruler;
fix the other ruler to the side of the desk in order to sign 7 cm from its start;
fill the tray with water until it reaches the 2 cm sign;
start recording with the phone on the tray’s side;
pull the tray up to 7 cm and drop it on the desk;
wait until the waves created hit the side opposite from the one you are standing in front of, and start the chronometer;
stop the chronometer when the waves hit the opposite side again;
stop recording;
repeat this process 2 more times with the same amount of water;
repeat steps 5-11 but with the different amounts of water (3,4,5,6) cm.

https://drive.google.com/drive/folders/186s4_7wogE54HAD6j-XP91iZ1rPl1m2a

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Theory Behind The Experiment

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Movement Of Waves

A wave always travels a y-z axis, varying the axis on the direction it is produced. For instance, if the wave is produced horizontally it will expand on a different axis than a wave produced in vertical. A wave can be considered a series of particles moving up and down an axis in series. Indeed a particle on many waves, creates a 360° motion, resulting in the particle to return back to the initial position. A particle, does not move of 360° in a circle, but remains on the same axis all the time.

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Mechanical Water Waves

Water Waves are transverse waves produced by the ocean, wind and movements on the ocean’s surface. Waves, being transverse, continue in a longitudinal and in a vertical way. Ocean waves also vary in wave speed based on the quantity of water there is in a determined space. The speed is based on the FRICTION it has on the seafloor, therefore the more the water the quicker the waves at the surface.

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Superposition

This is the process for which waves, based on their position and their meeting point, they can change their wavelength and their conditions. If the waves meet "in step", meaning that they are in the same position, they are amplified and they become greater. If instead two waves meet "out of step" they are cancelled out and the wave becomes a flat line, at 0°. With mechanical waves there is a higher possibility that they encounter each other out of step, being randomly produced and not in a string or line, but in a substance.

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Data Processing

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water depth (cm) +/- 0.1cm	time (s) +/- 0.01s [trial 1]	time (s) +/- 0.01s [trial 2]	time (s) +/- 0.01s [trial 3]
2	3,53	3,53	3,44
3	2,74	2,73	2,79
4	2,50	2,36	2,48
5	2,15	2,21	2,17
6	2,09	2,06	2,01

water depth (cm) +/- 0.1cm	average time (s) +/- 0.01s	absolute uncertainty (s) +/-0.01s
2	3,50	0,04
3	2,75	0,03
4	2,45	0,07
5	2,18	0,03
6	2,05	0,04

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Data Evaluation

The data we obtained confirmed our hypothesis. It showed that there is a higher wave speed in deeper water.

Moreover, our data had little error and enough difference between each depth. This validates our hypothesis even more and makes the experiment reliable.

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Research Question:

How will the water’s depth in the water tray affect the wave speed of the waves created by the motion imposed on the tray?

The data that we managed to collect supports our hypothesis, demonstrating that when there is less water in the tray, there is more friction with it, slowing down the waves, instead when there is more water there is less friction therefore quicker waves. The data we collected also helped us to answer our research question, as demonstrated above.

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Conclusions and Reflections

We think we carried out our experiment well, as shown by the little error, but we could definitely redefine some aspects of our work, especially by taking into account more details:

water spilled out of the tray
the different shapes/borders of the tray
carry out more trials for each measure
measure the time the wave took to travel a bigger distance

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What we learned from this experiment

We learned to work as a group without having any problem between ourselves;
this experiment can be used as baseline to understand movement of waves in the sea and the ocean;
we also expanded our knowledge on waves and friction alike.

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Bibliography

https://www.acs.psu.edu/drussell/Demos/waves/wavemotion.html

“Acoustics and Vibration Animations.” Longitudinal and Transverse Wave Motion, www.acs.psu.edu/drussell/Demos/waves/wavemotion.html.

https://www.bbc.co.uk/bitesize/guides/zgr8d2p/revision/2

“Adding and Cancelling Waves - Features of Waves - KS3 Physics Revision - BBC Bitesize.” BBC News, BBC, www.bbc.co.uk/bitesize/guides/zgr8d2p/revision/2.

https://courses.lumenlearning.com/boundless-physics/chapter/waves/

Boundless. “Boundless Physics.” Lumen, courses.lumenlearning.com/boundless-physics/chapter/waves/.

https://physics.stackexchange.com/questions/356287/why-does-the-speed-of-a-wave-travelling-in-shallow-water-increase-in-deep-water

MShMSh 3111 silver badge44 bronze badges, et al. “Why Does the Speed of a Wave Travelling in Shallow Water Increase in Deep Water?” Physics Stack Exchange, 1 Aug. 1967, physics.stackexchange.com/questions/356287/why-does-the-speed-of-a-wave-travelling-in-shallow-water-increase-in-deep-water.

https://www.physicsforums.com/threads/why-is-the-speed-of-water-waves-dependent-on-depth.411310/

quantum123. “Why Is the Speed of Water Waves Dependent on Depth?” Physics Forums | Science Articles, Homework Help, Discussion, Physics Forums | Science Articles, Homework Help, Discussion, 20 June 2010, www.physicsforums.com/threads/why-is-the-speed-of-water-waves-dependent-on-depth.411310/.