Resonance

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What is resonance?

The power of sound explained

The Sound Wave

It's common knowledge that sound is caused by a simple vibration of molecules. The faster the vibration, the higher pitch that we perceive. The unit for pitch, the Hertz (Hz), is just a measure of how many cycles a sound wave completes per second.

Besides from producing a pitch, sound waves have a height, or amplitude, that dictates the volume of the pitch that is produced. The higher the amplitude, the louder the pitch is.

Interference

Sound waves sometimes run into each other and cause an interference. These interferences affect the individual sound waves via a phenomenon called acoustic resonance. I won't go into it too much, but know that there is constructive (amplifying) and destructive (reducing) interference. The GIF above shows the resultant sound wave (in pink) from two interfering sound waves (in yellow and gray/blue).*

There's an interesting online simulator here to play more with interference. For the best results I would recommend wearing headphones and try inputting frequencies that are between 1-15 Hz apart or inputting the same frequency into both ears. (sound waves from the left and right speakers of your headphones/earbuds will interfere with each other to make different sound effects)

*There is a more detailed explanation of interference at the bottom of this page

Guitar D String Resonance.mp4

(Guitar string vibrates quietly at end of clip; it's hard to pick up the resonance with my microphone)

Resonant Frequency Introduction

An object's resonant frequency, also known as natural resonance or natural frequency, refers to the pitch at which that object will spontaneously react to. Sound waves at the correct Hertz level will excite an otherwise inert object and cause the object to vibrate at its resonant frequency. You can see this phenomenon in action with me singing into my acoustic guitar, to the left.

Resonant Frequency Derivation

I tried to predict the resonant frequency of my plastic water bottle with some water in it using the formula attached below the derivation.

To perform the calculations I had to assume the speed of sound was 343 m/s (which is the speed of sound at about 70° F) and that the plastic wouldn't significantly affect the resonant frequency. These are both not too unreasonable, but they definitely contributed to the percent error I had. Additionally, I could only estimate the bottle's actual resonant with about a 10Hz margin of error.

Still, given that a full piano ranges from about 27.5Hz to 4200Hz, I am quite satisfied with having only a 27.3% error given how small the numbers we are working with are (in the hundreds of Hertz).

A Small Tangent

It is theoretically possible to destroy ANY physical object, given you know the item's resonant frequency and have a loud enough speaker. A sound wave with an extremely high amplitude would so vigorously vibrate the object in question that it would rupture/shatter/burst from the energy of the sound waves.

Someone from NASA floated the idea that a sound of 1100 decibels would use enough energy to create a black hole that would swallow the entire universe...

Interference (cont.)

When two or more sound waves intersect through any medium, they interfere each other's amplitudes. Interfering waves create a resultant wave whose amplitude is always the sum of all the individual interfering waves.

It is important to note that sound waves will never modify each other's base frequency or speed. The only change that occurs is in amplitude, and thus perceived loudness.

For instance, noise cancelling headphones operate by detecting outside ambient noise then creating sound waves that are exact opposites of the detected sound waves. The crest of the detected sound wave will be the trough of the created sound wave, and vice versa. This reduces or even fully "cancels" any noise one would normally perceive.

Pictured: a standing wave with nodes and antinodes labeled. One cycle (aka the wavelength) of the standing wave is also labeled.

Intro to Standing Waves

We'll get more into standing waves in the harmonics section, but for now we will see how resonance causes this acoustic phenomenon:

When two identical sound waves moving in opposite directions interfere with each other, they construct a standing wave. The resulting wave will have both nodes (points on the wave with zero vibration) and anti-nodes (points on the wave with maximum vibration, 2x the amplitude of one of the individual sound waves).

Most commonly, waves inside a container vibrating at that container's resonant frequency will create standing waves. These standing waves are the basis for harmonic overtones, which are discussed in the Harmonics page.

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