Phase (waves)

FIELDS OF STUDY: Acoustics; Electromagnetism; Classical Mechanics

ABSTRACT: This article defines and describes phase as it relates to waves. Waves can interfere with each other to produce waves with increased or decreased amplitudes. This interference is useful for many applications, including increasing or reducing sound intensities.

Principal Terms

• antiphase: a 180-degree or π-radian phase difference.
• constructive interference: when two or more waves of the same phase combine to form a larger amplitude.
• destructive interference: when two or more waves of different phases combine to form a smaller amplitude.
• instantaneous phase: the time-variant angle of a sinusoidal function.
• phase offset: also called phase difference; the time interval or phase angle that results when one wave is ahead of or behind another.
• pi: the ratio of the circumference of a circle to its diameter, symbolically represented as π. Its numerical value is approximately 3.14159.
• sinusoidal function: a curve that is like a sine wave but experiences a shift in amplitude or phase.

The Phase of a Wave

The phase of a wave denotes the current location of a wave relative to a reference point. Amplitude (A), frequency (f), and phase (φ) of a wave can be related by the sinusoidal function

where π is pi and t is time. Phase can also be used to refer to the time-variant angle (2πft + φ), or instantaneous phase.

A phase difference, or phase offset, occurs when waves of the same frequency travel ahead of or behind each other. Two waves with same frequency are considered in phase with each other if they have no phase difference and out of phase if they have a phase difference. Phase offset can be expressed in degrees or radians, with 360 degrees (2π radians) indicating one wavelength.

Interference

Superposition occurs when two or more waves combine to form a wave displacement equal to the sum of the individual waves’ displacements. Consider two waves traveling with the same amplitude, frequency, and wavelength in the same direction. Constructive interference occurs when the two waves are in phase with each other and produces a resulting wave with an amplitude equal to twice that of the individual waves. Destructive interference occurs when the two waves are antiphase and the waves cancel out. This total displacement of zero results because the positive displacement of one wave momentarily adds to the negative displacement of the second. When dropping stones in a pond, for example, the ripples moving outward from the stones interfere constructively in some places to produce a wave that has greater amplitude and, in other places, interfere destructively to produce an area that appears undisturbed. Destructive interference is commonly used to reduce the intensity of noise in places such as an airplane cabin.

Bibliography

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Hass, Jeffrey. "What Is Phase?" Acoustics Primer. Center for Electronic and Computer Music, Indiana U, Bloomington, 2003. Web. 20 May. 2015.

Herman, Russell L. A Course in Mathematical Methods for Physicists. Boca Raton: CRC, 2014. Print.

"Interference of Waves" Physics Classroom.Physics Classroom, 1996–2015. Web. 20 May. 2015.

National Geographic Society. The Science of Everything: How Things Work in Our World. Washington: Natl. Geographic Soc., 2013. Print.

Walker, James S. Physics. 5th ed. San Francisco: Pearson Education, 2010. Print.