This set of results successfully confirms that the water wave does travel at a constant speed, because the distance of the tank clearly stays the same throughout, and the time taken for the wave to travel this certain distance stays constant (as, for example, the time taken for one ripple bounce is equal to half the time taken for two ripple bounces) so therefore the speed (which is distance ÷ time) must also stay steady. So the distance-time graph representing these results would be a straight line passing through the origin (see below), thus indicating steady speed. This preliminary work also proves that the height from which the tank is dropped does not matter, because the speed of the water wave is the same anyway. Here is a sketch graph of the speed obtained for the preliminary work results:
PREDICTION
My prediction is that as the quantity (depth) of water increases, the waves will travel more quickly, until about 2.5cm, when the best-fit lines begin to go into a plateau. The reasons for this are explained below, in ‘Scientific Knowledge’.
I expect the graph of time and water depth to be plotted like so:
I expect the graph of speed and water depth to look like this:
SCIENTIFIC KNOWLEDGE
To support my prediction, I will have to state some scientific knowledge. The amplitude of a wave is simply the size of the wave. However, with less water, the waves are more likely to have friction acting against them, especially when the amplitude of the wave causes it to scrape along the bottom of the tank. With increasing amounts of water, the friction is reduced and therefore the waves travel a lot faster.
A water wave (like the one we are investigating in this practical) is usually said to be a transverse wave, like this:
In the above diagram, the energy is being transferred from left to right, but the particles of the water are only moving up and down. Therefore this is a transverse wave: the direction of the particle oscillations is at 90° to the direction of the energy transfer. However, some mechanical wave motions, such as waves on the surface of a liquid, are combinations of both longitudinal and transverse motions (neither wholly transverse nor longitudinal), resulting in a roughly circular motion of particles of the liquid. This is what we are seeing in our experiment.
For a transverse wave, the wavelength (λ) is the distance between two successive wave crests or troughs. Many other points on a wave are also a wavelength apart; at such points the particles are moving in the same direction, and with the same speed. They are described as being “in phase”. (But for longitudinal waves, it is the distance from compression to compression or from rarefaction to rarefaction.) The frequency of the wave is the number of vibrations per second. The velocity of the wave, which is the speed at which it advances, is equal to the wavelength multiplied by the frequency. The maximum displacement involved in the vibration of a mechanical wave is the amplitude of the wave.
Small-wavelength water waves (λ ≈ 10mm) are ripples. They depend on the surface tension of the water surface for their elastic property. Typical speeds in ripple tanks with water of different depths are 0.2ms-1 to 0.3ms-1.
In shallow water, waves generated at a particular frequency travel more slowly than in deep water. The frequency is fixed by the oscillation frequency of whatever causes the original disturbance to produce the wave (i.e. here it is the dropping of the tank).
speed of wave = frequency × wavelength
v = f × λ
And, since v = f × λ, and f is the same in both cases of shallow and deep water, then, as the velocity is reduced, so is the wavelength.
Also, in shallow water (for example, water in ripple tanks) the speed of water waves in equal to √gh, and so depends on the depth of the water, h. So for these waves:
speed of wave = √gh
(where g = acceleration due to gravity (ms-2), h = depth of shallow water (m)
So what will happen in the tank in our practical? For water depths such as 0.5cm and 1.0cm, the water wave (produced by the dropping of tank) will scrape the bottom of the tank, but there will be a depth from where it is as if the bottom was just not there, because the troughs of the wave do not even reach the bottom. Therefore the speed of the water wave will increase as it experiences less and less friction against the bottom of the tank for the lower water depths, but then once the depth at which the wave does not touch the bottom is reached, the speed will just stay the same regardless of how much more water is added (and so the graphs have plateaux).
But for the experiment to be fair and successful, there are a number of key factors:
- using the same plastic tank for each test, so that the distance the water wave has to travel for one ‘bounce’ is always exactly the same;
- keeping one’s eye position constant during each test (otherwise one would observe the waves bouncing off from a different angle of eyesight, so the reaction time for the wave bouncing would be different for each bounce, making the results slightly wrong);
- measuring each water depth carefully with a rule from the same point each time, i.e. with the bottom end of the rule resting on the bottom of the tank (see ‘Diagram’, pg. 1);
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ensuring that the forefront of the ripple touching the sides of the tank was used for the starting and stopping of the stopwatch every time, and therefore the experiment was kept fair and the results were more accurate.