Wave Phenomena and Electric Charge Principles
Principle of Superposition: When two or more waves propagate through a medium, the resulting disturbance at each point of the medium is equal to the sum of the disturbances each wave would have spread in isolation. y = y1 + y2.
Interference: Phenomenon that occurs when two wave motions are coincident (in space and time). Interference leads to areas with intensified wave motion and areas with weakened wave motion. The former are the constructive interference in which the amplitude of the resultant wave is maximal and equal to twice the amplitude of the component waves. Constructive interference occurs when the difference in the points of travel of the waves is 0 or an integer number of wavelengths. Waves arrive in phase at these points. Destructive interference is characterized by zero amplitude for all points where the difference in the travel of the waves is an odd number of half wavelengths. The waves are in opposition phase at these points.
Standing Waves: They are a special case of interference, occurring when two identical wave motions move in opposite directions. The resulting wave produces the sensation of not moving, a stationary situation in motion with a fixed amplitude at each point in space. Standing waves present zero amplitude points called nodes and maximum amplitude points called bellies. The resulting wave equation is: Y = 2A cos(ωt) sin(kx).
Standing waves occur when space limits wave propagation, and at these limits, there is a reflected wave of the same frequency traveling in the opposite direction. These limits can be fixed or free. A fixed limit can be a string with one end fastened to a wall, and a free limit may be the open end of a sound tube. Certain frequencies result in standing waves and are called resonant frequencies. The lowest resonant frequency, leading to a wave with the longest wavelength, is called the fundamental frequency and corresponds to the first harmonic. The second frequency will produce the second harmonic, which is twice the first, and the wavelength is half that of the first harmonic.
Huygens’ Principle: Each point on a wavefront acts as a source emitting secondary spherical wavelets, and the envelope of these wavelets constitutes the new wavefront. A wavefront is the surface formed by all points reached by a wave at the same time. Therefore, all points on the wavefront will have the same phase.
Wave diffraction occurs when a wave encounters an obstacle whose size is of the same order of magnitude as its wavelength. We can observe the diffraction of waves in surface water by placing two connected tanks with a small opening. Producing a disturbance in one tank, the wave propagates to the other tank through the opening, following Huygens’ principle.
Refraction of waves is based on the change of direction of propagation when a wave moves to a different medium, such as sound traveling from air to water. If the medium does not allow the propagation of the wave, we call it an opaque medium.
Reflection of waves is based on the change of direction of wave propagation at the boundary between two different media. After reflection, the wave continues its propagation in the same medium. A clear example is the reflection of light in a mirror.
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The electric charge is always a multiple of an electron’s charge. There is no free charge that is half the charge of an electron; such a particle would be the electron’s antiparticle. The electric charge is conserved in all observed physical processes. In electrification processes, no net charges are created. Electrons are transferred but not created or destroyed.
Coulomb’s Law: The force of attraction or repulsion between two electric charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
Characteristics of electrical forces:
- The force acts along the line joining the charges.
- The force is repulsive if the charges have the same sign and attractive if the charges have opposite signs.
- Electrical forces are distance forces; they do not need any material medium between the charges to act.
- They always appear in pairs, as stated in Newton’s 3rd Law (the principle of action and reaction).
- Electrical forces obey the superposition principle.
Electric Field: A region of space surrounding a charge, such that if another charge is placed in this region, it experiences a force of attraction or repulsion depending on the sign of the charges. The electric field is described by the field strength (also called electric field intensity) and by the electric potential, which is related to the energy of a charge located at a point in the field.
Intensity: The magnitude is given by… The direction is along the line connecting the source charge and the point of interest. The sense is that of the force experienced by a positive test charge at that point. Units: N/C. If we have a point charge, the formula is F = qE.