- Point particle: object whose size is irrelevant, so you can assume that all the mass was in a point. For example, a car that goes from Rome to Florence can be considered a point particle because it is very small compared to the distances covered.
- Trajectory: line along which a point particle moves.
- Uniform circular motion: that of a point particle moving along a circumference (circular) move through the same distance in the same time (uniform).
- Simple harmonic motion: if a point P has an uniform circular motion, its orthogonal projection Q on any diameter of the trajectory has a motion that is called simple harmonic. It is a periodic motion that consists of the oscillation of Q between the extremes of the diameter.
The equation of the simple harmonic motion is
x=Rsin(ωt+α0),where:
- x is the x-coordinate of the point Q, and determines its position on the diameter as a function of time;
- R is the radius of the circumference, and is called amplitude;
- ω is the ratio of angle traversed by P (i.e., if the point moves from P to P’ and O is the center of the circumference, the angle POP’) and the time it takes; it is called the pulsation of the simple harmonic motion;
- t is the time;
- α0 is the measure of an angle, and is called initial phase (more generally, ωt+α0 is the phase at time t).
- x is the x-coordinate of the point Q, and determines its position on the diameter as a function of time;
- Complete oscillation: the one performed by a point that moves in simple harmonic motion when go back to one end of the diameter from which it is started. The distance traveled is then equal to twice the diameter.
- Equilibrium position: the one in which a point particle, initially at rest, remains at rest.
- Wave: region of space where each point oscillates (for example with a simple harmonic motion), inducing, normally with some delay, oscillations in near points. This is what happens to the sea surface, where each molecule oscillates vertically, causing by, friction, similar oscillations to neighboring molecules. Note that a wave results in a movement of energy, and NOT of matter, that instead only oscillates around a central equilibrium position.
The simplest equation of a progressive wave (i.e. that propagates along the positive x-axis) is
y=Asin[2π(t/T-x/λ)+α0],where:
- y is the distance from the equilibrium position of a single point (in the case of sea waves, the height of water at a single point and at a given time minus that of the sea when it is calm);
- A, called wave amplitude ,is the maximum distance of a point from its equilibrium position;
- π is the ratio between the length of a circle and that of its diameter, and it is approximately 3.1415926;
- t is the time;
- T is the time taken by a point that is in the highest position to come back the next time and is called period of the wave;
- x is the x-coordinate of the point (for sea waves, its distance from the shore);
- λ, said wavelength, is the distance between two consecutive maxima or minima (for example, between two successive rollers);
- α0 is an angle, said initial phase.
y=Asin[2π(t/T+x/λ)+α0].From these two equations you can deduce that all points reached by the wave move in simple harmonic motion, but are phase-shifted: in other words, when one is in a maximum, another one is in its equilibrium position, yet another is in a minimum, and so on.
Progressive wave Regressive wave
In the figures above you can see that, while individual points oscillate vertically, the wave propagates to the right (progressive wave) or left (regressive wave). - y is the distance from the equilibrium position of a single point (in the case of sea waves, the height of water at a single point and at a given time minus that of the sea when it is calm);
- Frequency of a wave:
how many times, in a second, a point reached by the wave completes a complete oscillation. It is also equal to how many wavelengths the wave propagates in a second.
- Reflection: phenomenon whereby a wave, encountering an obstacle, at least partially go back (like light waves when you look in the mirror). In particular a progressive wave, after reflection, becomes regressive.