resultant wave
Summary
A resultant wave is the single wave formed when two or more waves overlap in the same medium. At each point its displacement is the sum of the individual displacements (superposition). In-phase waves give a larger amplitude, and waves 180° out of phase give a smaller one.
Detail
Meaning: A resultant wave is the single wave formed when two or more waves overlap in the same medium. By superposition, the displacement at each point is the sum of the individual displacements. Waves that are in phase give a larger amplitude (constructive interference). Waves 180° out of phase give a smaller one (destructive interference), which cancels completely if the amplitudes are equal.
Equation: y = y₁ + y₂, where y is the resultant displacement and y₁ and y₂ are the individual displacements at the same point and time (all in m for a string wave).
On the MCAT: Passages use two speakers, two slits, or two strings. For sources in phase, a path difference of nλ gives constructive interference and a path difference of (n + ½)λ gives destructive interference, where n is an integer and λ is the wavelength in m. Questions may ask you to add two pulses graphically. They may also link standing waves and beats to superposition. The beat frequency is |f₁ − f₂|, with f in Hz.
Common confusion: Waves do not permanently change or destroy each other. In the ideal case they pass through one another and emerge unchanged, and only the overlap region shows the sum. Destructive interference at one point does not mean energy is lost. The energy is redistributed to regions of constructive interference.
Sources
- Physics (Cutnell and Johnson)
- Fundamentals of Physics (Halliday, Resnick, and Walker)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.