Wave Interaction: Superposition and Interference Quiz

PDF page 414: Most waves appear complex because they result from two or more simple waves that combine as they come together at the same place at the same time—a phenomenon called superposition. Waves superimpose by adding their disturbances; each disturbance corresponds to a force, and all the forces add. If the disturbances are along the same line, then the resulting wave is a simple addition of the disturbances of the individual waves, that is, their amplitudes add.

PDF page 418: c. By adding their disturbances

PDF page 414: The two special cases of superposition that produce the simplest results are pure constructive interference and pure destructive interference. Pure constructive interference occurs when two identical waves arrive at the same point exactly in phase. When waves are exactly in phase, the crests of the two waves are precisely aligned, as are the troughs. Refer to Figure 13.11. Because the disturbances add, the pure constructive interference of two waves with the same amplitude produces a wave that has twice the amplitude of the two individual waves, but has the same wavelength.

PDF page 415: pure destructive interference. Because the disturbances are in opposite directions for this superposition, the resulting amplitude is zero for pure destructive interference; that is, the waves completely cancel out each other.

PDF page 415: Figure 13.12 shows two identical waves that arrive exactly out of phase—that is, precisely aligned crest to trough—producing

PDF page 415: pure destructive interference. Because the disturbances are in opposite directions for this superposition, the resulting amplitude is zero for pure destructive interference; that is, the waves completely cancel out each other.

PDF page 416: Sometimes waves do not seem to move and they appear to just stand in place, vibrating. Such waves are called standing waves and are formed by the superposition of two or more waves moving in opposite directions. The waves move through each other with their disturbances adding as they go by. If the two waves have the same amplitude and wavelength, then they alternate between constructive and destructive interference. Standing waves created by the superposition of two identical waves moving in opposite directions are illustrated in Figure 13.14.

PDF page 418: a. Standing waves are formed by the superposition of two or more waves moving in opposite directions.

PDF page 417: produce standing waves may be due to the reflections from the side of the glass. Earthquakes can create standing waves and cause constructive and destructive interferences. As the earthquake waves travel along the surface of Earth and reflect off denser rocks, constructive interference occurs at certain points. As a result, areas closer to the epicenter are not damaged while areas farther from the epicenter are damaged. Standing waves are also found on the strings of musical instruments and are due to reflections of waves from the ends of the string. Figure 13.15 and Figure 13.16 show three standing waves that can be created on a string that is fixed at both ends. When the wave reaches the fixed end, it has nowhere else to go but back where it came from, causing the reflection. The nodes are the points where the string does not move; more generally, the nodes are the points where the wave disturbance is zero in a standing wave. The fixed ends of strings must be nodes, too, because the string cannot move there. The antinode is the location of maximum amplitude in standing waves. The standing waves on a string have a frequency that is related to the propagation speed of the disturbance on the string. The wavelength is determined by the distance between the points where the string is fixed in place.

PDF page 417: produce standing waves may be due to the reflections from the side of the glass. Earthquakes can create standing waves and cause constructive and destructive interferences. As the earthquake waves travel along the surface of Earth and reflect off denser rocks, constructive interference occurs at certain points. As a result, areas closer to the epicenter are not damaged while areas farther from the epicenter are damaged. Standing waves are also found on the strings of musical instruments and are due to reflections of waves from the ends of the string. Figure 13.15 and Figure 13.16 show three standing waves that can be created on a string that is fixed at both ends. When the wave reaches the fixed end, it has nowhere else to go but back where it came from, causing the reflection. The nodes are the points where the string does not move; more generally, the nodes are the points where the wave disturbance is zero in a standing wave. The fixed ends of strings must be nodes, too, because the string cannot move there. The antinode is the location of maximum amplitude in standing waves. The standing waves on a string have a frequency that is related to the propagation speed of the disturbance on the string. The wavelength is determined by the distance between the points where the string is fixed in place.

PDF page 420: antinode location of maximum amplitude in standing waves constructive interference when two waves arrive at the same point exactly in phase; that is, the crests of the two waves are precisely aligned, as are the troughs destructive interference when two identical waves arrive at the same point exactly out of phase that is precisely aligned crest to trough inversion vertical flipping of a wave after reflection from a fixed end longitudinal wave wave in which the disturbance is parallel to the direction of propagation mechanical wave wave that requires a medium through which it can travel medium solid, liquid, or gas material through which a wave propagates nodes points where the string does not move; more generally, points where the wave disturbance is zero in a standing wave periodic wave wave that repeats the same oscillation for several cycles and is associated with simple harmonic

PDF page 417: produce standing waves may be due to the reflections from the side of the glass. Earthquakes can create standing waves and cause constructive and destructive interferences. As the earthquake waves travel along the surface of Earth and reflect off denser rocks, constructive interference occurs at certain points. As a result, areas closer to the epicenter are not damaged while areas farther from the epicenter are damaged. Standing waves are also found on the strings of musical instruments and are due to reflections of waves from the ends of the string. Figure 13.15 and Figure 13.16 show three standing waves that can be created on a string that is fixed at both ends. When the wave reaches the fixed end, it has nowhere else to go but back where it came from, causing the reflection. The nodes are the points where the string does not move; more generally, the nodes are the points where the wave disturbance is zero in a standing wave. The fixed ends of strings must be nodes, too, because the string cannot move there. The antinode is the location of maximum amplitude in standing waves. The standing waves on a string have a frequency that is related to the propagation speed of the disturbance on the string. The wavelength is determined by the distance between the points where the string is fixed in place.

PDF page 417: As we saw in the case of standing waves on the strings of a musical instrument, reflection is the change in direction of a wave when it bounces off a barrier, such as a fixed end. When the wave hits the fixed end, it changes direction, returning to its source. As it is reflected, the wave experiences an inversion, which means that it flips vertically. If a wave hits the fixed end with a crest, it will return as a trough, and vice versa (Henderson 2015). Refer to Figure 13.17.

PDF page 417: If the end is not fixed, it is said to be a free end, and no inversion occurs. When the end is loosely attached, it reflects without

PDF page 418: Rather than encountering a fixed end or barrier, waves sometimes pass from one medium into another, for instance, from air into water. Different types of media have different properties, such as density or depth, that affect how a wave travels through them. At the boundary between media, waves experience refraction—they change their path of propagation. As the wave bends, it also changes its speed and wavelength upon entering the new medium. Refer to Figure 13.18.

PDF page 418: For example, water waves traveling from the deep end to the shallow end of a swimming pool experience refraction. They bend in a path closer to perpendicular to the surface of the water, propagate slower, and decrease in wavelength as they enter shallower water.