Sound Wave Addition

Sound wave addition is the phenomenon by which two or more waves superimpose at a point, their amplitudes adding algebraically to produce a resultant wave.

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How to measure it in class

With the FizziQ app, it is possible to study the addition of two sound waves and measure the increase in sound level.

Steps:

Open FizziQ on a first smartphone and select the sound level meter (sound level in dB). Place a sound source (speaker or second smartphone emitting a continuous sound) at 30 cm and note the measured level.
Add a second identical sound source next to the first, at the same distance. Measure the new sound level and calculate the difference.
Verify that the increase is approximately 3 dB (and not a doubling in dB). Explain why using the logarithmic property of the decibel scale.
To observe interference: use two speakers emitting the same pure frequency and move the smartphone between them. Identify positions of sound reinforcement and attenuation.

Scientific activities on this topic

Many experiments can be easily done with a smartphone to understand sound wave addition phenomena.

Addition of two noises of the same intensity
Analysis of acoustic beat phenomenon: https://www.fizziq.org/en/activities/acoustic-beats/
Spatial interference of two waves of the same frequency: https://www.fizziq.org/en/activities/a-bubble-without-noise/

Learn more

It is often said that if two sounds of the same sound intensity are added, the resulting wave will see its intensity increase by 3 decibels. In fact, as we explain in this article, this result is only true in the particular case of noise, and we can see through this simple example the complexity of the wave addition process.

Below we detail certain elements to consider when studying the sound wave addition process:

Wave superposition: According to the wave superposition principle, when two sound waves are added, the resulting acoustic pressure at a given point is the sum of the individual acoustic pressures of the two waves at that point.
Interference: When two sound waves combine, they can interact in different ways. Interference can be constructive, where waves add together to create a larger resultant wave, or destructive, where they subtract to create a smaller resultant wave.
Phase: The relative phase between two sound waves plays a crucial role in interference. If waves are in phase (that is, their peaks and troughs coincide), they can reinforce each other. If they are in anti-phase (that is, their peaks and troughs cancel each other out), they can cancel each other.
Amplitude: The amplitude of sound waves determines sound intensity. When you add sound waves, you also add their amplitudes, which can result in an increase in sound volume.
Frequency: The frequency of sound waves determines their tonal pitch. If you add waves of different frequencies, you will get a combination of frequencies that can create harmonics and complex timbres.

Wave addition is a very interesting process to study in class because tools such as smartphones allow quickly performing experiments that put theoretical concepts learned into practice.

Formula

For two waves of the same frequency and amplitude, the resulting pressure depends on the phase difference:

p_total = 2 x A x cos(delta_phi / 2) x cos(omega*t + phi_mean)

Meaning: p_total: resulting acoustic pressure (Pa) A: amplitude of each wave (Pa) delta_phi: phase difference between the two waves (rad) omega: angular frequency (rad/s) t: time (s) phi_mean: mean phase of the two waves (rad)

For decibel addition of two incoherent sources of the same level: L_total = L + 10 x log10(2) = approximately L + 3 dB

Application examples

Active noise-canceling headphones that generate a sound in anti-phase to cancel ambient noise
Beats perceived when two instruments play notes that are very slightly out of tune
Silent zones in a concert hall due to interference between direct and reflected waves
The sound of a tuning fork that varies in intensity when rotated near the ear
Sound vibrations in an organ pipe, the result of adding forward and backward waves

FAQ

Q: Why do two 60 dB sources not make 120 dB? A: Because decibels use a logarithmic scale. Intensities (powers) are added, not decibels. Two identical sources double the intensity, which corresponds to an addition of only 3 dB.

Q: Can two sounds completely cancel each other? A: Yes, if two waves of the same frequency and amplitude arrive in perfect anti-phase. This is the principle used by active noise-canceling headphones. In practice, cancellation is never perfect.

Q: What is an acoustic beat? A: It is the phenomenon that occurs when two sounds of very close frequencies superimpose. The resulting sound fluctuates in intensity at a frequency equal to the difference of the two frequencies, creating a pulsation effect.

Q: Does wave addition work for light? A: Yes, the superposition principle applies to all waves. Light interference, like that observed in Young’s double-slit experiment, is the exact optical analog of sound wave addition.

Q: How does active noise reduction work? A: A microphone captures external noise. A processor calculates in real time the inverse signal (in anti-phase). A speaker emits this inverse signal, which adds to the noise and attenuates it through destructive interference.

Interference - Acoustic beats - Superposition principle - Sound level - Decibel - Standing wave - Active noise reduction