Reflection & Standing waves 1-d and 2-d waves

Wavefront vs ray Wavefront: The actual 2-d wave that we see moving Ray: The “vector”, drawn perpendicular to the wavefront, that shows the direction in which the wave is propagating (transfering energy)

Huygen’s principle

Law of Reflection The angle of incidence is equal in magnitude to the angle of reflection The reflected and refracted rays are in the same plane as the incident ray and the normal.

Reflection: 1-d waves off free end End of medium is still able to be moved Reflected pulse is upright (same orientation as the incident pulse)

Reflection off fixed end End of medium is immovable Reflected pulse is inverted relative to the incident pulse

Superposition of waves The adding of wave amplitudes when two waves meet The energy from each wave will have a combined affect on the position (movement) of the particle in the medium Waves pass through each other and are not individually affected

Constructive interference Occurs when both waves have displacements in the same direction at the point where they meet (i.e. crest meeting crest, compression meeting compression)

Destructive interference Occurs when waves with opposite displacements meet each other i.e. crest meeting trough; compression meeting rarefaction If amplitudes are equal, but opposite, then total destructive interference will occur—combined amplitude = 0

Standing waves (section 4.5) When a traveling wave reaches a fixed or free-end boundary, it reflects upon itself. Through the principle of superposition, constructive and destructive interference will occur IF the frequency is just right so that the reflected wave has maximum and minimum displacements that are always in the same position, a standing wave has formed

Standing waves Node: An area of constant total destructive interference. The amplitude of the medium at this point is zero, even though there are waves passing by that point in each direction. The amplitudes of the incident wave and the reflected wave are always exact opposites of each other, resulting in a zero net amplitude

Standing waves Antinode: An area of maximum constructive interference. The amplitude of the medium at this point reaches the maximum value, and alternates between positive and negative. The amplitude of both the incident wave and the reflected wave are consistently in the same direction (i.e. crest meets crest, trough meets trough)

Harmonics Standing waves will form at many different frequencies Any time the wavelength (or half a wavelength) will fit in the length of the string in some multiple, a standing wave will form Fundamental Frequency (first harmonic): Equivalent to the natural frequency of the medium Results in one half-wavelength to form a standing wave in the medium