Phase Shift

Phase shift is the temporal or angular offset between two oscillations of the same frequency, expressed in radians or as a fraction of the period.

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How to measure it in class

Steps:

Use two smartphones emitting a pure tone at the same frequency (e.g., 440 Hz) using FizziQ’s sound library.
Place both smartphones side by side facing a third smartphone measuring sound level. Verify the sound is amplified (the two sources are in phase).
Gradually move one smartphone away. Observe sound level variations on the third device: sound decreases when the two sources become out of phase.
Interpret: when the path difference corresponds to a half-wavelength, the two waves arrive in opposite phase and partially cancel.

Scientific activities on this topic

Several experiments easily performed with a smartphone, tablet, or computer allow you to observe and understand phase shift between two waves.

1: A Bubble of Silence - How does active noise cancellation technology work in headphones?: https://www.fizziq.org/en/activities/a-bubble-without-noise/

2: Acoustic Beats - How the acoustic beat effect is used in electronic music: https://www.fizziq.org/en/activities/acoustic-beats/

3: Addition of Sound Waves - What is the increase in sound level when adding two waves of the same intensity?: https://www.fizziq.org/en/activities/addition-of-sound-waves/

4: Doppler Effect - Measuring the Doppler effect using FizziQ’s sound library: https://www.fizziq.org/en/activities/doppler-effect/

Learn more

Historical context:

The concept of phase shift developed in the 19th century with Augustin Fresnel, who used phase differences to explain light diffraction patterns. His work definitively confirmed the wave nature of light and introduced interference calculations.

Phase shift and beats:

When two sounds of slightly different frequencies superimpose, their relative phase shift continuously changes. This produces the beat phenomenon: the sound seems to oscillate between loud and soft. Musicians use this to tune their instruments.

Technological applications:

Phase shift is central to many technologies: phased array antennas (radar, 5G) orient their beam by controlling phase shift between network elements. Audio filters exploit phase shift to select or reject frequencies.

Additional experiments:

The experiment A Bubble of Silence concretely illustrates how phase shift is used in active noise-canceling headphones.

Formula

φ = 2π × Δt / T

Where:

φ: phase shift (rad)
Δt: time delay between the two signals (s)
T: common period of both signals (s)

For two points on the same wave separated by distance d: φ = 2π × d / λ

Where:

d: distance between the two points (m)
λ: wavelength (m)

Application examples

Noise-canceling headphones create a sound in opposite phase to ambient noise to cancel it
In stereo, a slight phase shift between the two speakers creates the sensation of sound spatialization
Phaser and flanger in electronic music are effects produced by variable phase shift
Parabolic antennas adjust signal phase shift to point in a precise direction
Two speakers wired in opposite phase produce weak sound because the waves partially cancel

FAQ

Q: What are signals in phase? A: Two signals are in phase when they oscillate at exactly the same rhythm and at the same moment. Their phase shift is zero (0 rad). When they superimpose, they add together and produce a signal with double amplitude.

Q: What is opposite phase? A: Two signals are in opposite phase when their phase shift is π rad (180°). When one is at its maximum, the other is at its minimum. Their superposition produces a signal with reduced amplitude, or even zero.

Q: How do noise-canceling headphones use phase shift? A: The headphones capture ambient noise, then emit an identical sound but in opposite phase (phase shift of π). The two waves cancel, considerably reducing perceived noise.

Q: Does phase shift depend on frequency? A: Phase shift between two points of a wave depends on the distance between those points and the wavelength, thus indirectly on frequency. For the same distance, a high-pitched sound has a greater phase shift than a low-pitched sound.

Q: How do you measure a phase shift? A: You measure the time delay Δt between the two signals on an oscillogram, then calculate φ = 2π × Δt / T.

Interference - Wavelength - Path difference - Sound wave - Superposition - Beats