Investigating the speed of travelling waves in water.

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Physics Coursework Assignment 2                                          Christabel Adebayo

Investigating the speed of travelling waves in water.

Aim

The objective of this experiment is to investigate how the speed of travelling waves in water varies with the depth of water, and to verify whether the results supports the formula v2 = gd.

Background knowledge

Mechanical Waves are waves, which propagate through a material medium (solid, liquid, or gas) at a wave speed, which depends on the elastic and inertial properties of that medium. There are two basic types of wave motion for mechanical waves: longitudinal waves and transverse waves.

In a longitudinal wave the particle displacement is parallel to the direction of wave propagation. The particles simply oscillate back and forth about their individual equilibrium positions.

In a transverse wave the particle displacement is perpendicular to the direction of wave propagation. The particles do not move along with the wave; they simply oscillate up and down about their individual equilibrium positions as the wave passes by.

Water waves are an example of waves that involve a combination of both longitudinal and transverse motions. As a wave travels through the waver, the particles travel in clockwise circles. The radius of the circles decreases as the depth into the water increases.

If the radius of the circles decreases, this means that the wavelength of the wave increases. If the wavelength increases, the speed of the wave therefore increases.  This can be seen from the formula; - v = f * λ

Where v = speed, f = frequency, and λ = wavelength.  The speed of the wave is directly proportional to the wavelength.  

For that reason, I predict that the speed of the wave increases, as the depth increases.  The relationship between these is given by the theory, which suggests that the speed of a waves on water is given by; - v2= g*d   (where, v = speed of wave, g = acceleration of gravity and d = depth of water).

This shows that the speed (squared) is directly proportional to the depth of water.

Preliminary measurements

Before proceeding to find the wave velocity, I will need to measure the length and width of the tray and to see whether it is flat on the bottom.  The length of the base of the tray is 37.5cm.  The width is 22.5 cm and the total depth is 8cm.  Since the depth of the tray is 8cm, this will limit me to investigate up to a maximum depth of 4cm.  This is so that, the water does not spill or overflow when lifted up.  In order to gain a range of results, I will investigate depths of every 0.5cm, starting with 0.5cm, then 1cm, afterwards 1.5cm and so forth, until 4cm. A considerable range of results is needed as this will improve accuracy and will provide more evidence to support my hypothesis. I am measuring in cm, as this is the standard international (S.I) unit that should be used.

  In order to find out if the bottom of the tray is flat, when the water of depth 0.5cm is poured into tray, I will take measurements of the depth of water at either end and at the centre of the tray.  The measurements should all be at 0.5cm. If the values are different, then this means that the bottom of the tray is not flat.  It is important that the bottom of the tray is flat because if not, then the depth of the water that the waves travel will vary.  This will make the investigation unfair and inaccurate, as the depth must remain constant throughout the whole plane, as this is the variable in the experiment.

The sides of the tray slightly slope outwards.  This is a slight disadvantage, as it may affect the accuracy of the results.

Apparatus

Plastic apparatus tray

Cold tap water

Stop clock

Setsquare

Ruler

A book

Marker Pen

Set-up

Method

Fill an apparatus tray with 0.5cm of water.  In order to measure 0.5cm of water accurately a setsquare can be used. The shorter side of the setsquare can be placed on the base of the inside of the tray, and the longer side will be used to measure the depth of the water.

In order to set off a wave, the tray needs to be lifted up and then set down.  The tray will be lifted up by one of the shorter sides 2cm high and then gently lowered again.  In order to ensure that the side of the tray is lifted to exactly 2cm, I will use a ruler to measure this height.  It will be very awkward and tricky to hold the ruler, whilst lifting the tray at the same time; therefore, the ruler can be taped to the spine of a book to hold it up.  This way, I can suitably lift up the tray without any complexity and difficulty.

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It is important that the tray is always lifted to 2cm, because this will make sure that the investigation is fair.  It will also make sure that there is only one variable in the experiment, which is the depth of water.

When the tray is lowered, it will be done by hand at an even uniform speed.  Obviously, the speed in which this is achieved; every time the tray is lowered will not always be identical, but a general similarity in speed will be attained.

Consequently, this should not cause a major problem in this investigation.

When the tray is ...

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