# Help me understand resonance

I don't fully understand how resonant chambers work. My confusion stems from the fact that the chambers are passive elements or filters, yet somehow are able to amplify the sound.

Questions:

1. How can I differentiate between passive objects that can amplify a source and ones that can't? Where is the connection? Why can I add a chamber to a violin and it gets louder, but building a wall in front of it diminishes the sound.

2. Do the resonant chambers vibrate / produce sound themselves or merely aid a string or other tone producing objects in vibration IE. Does a string make a louder sound because of the chamber, or are we hearing a combination of faint string plus a much louder chamber? Put in yet a other way, does the resonator move the primary point source of the sound?

My current understanding on the matter is that the chamber actually does not amplify the tone as function of it's resonant nature. Rather, what is tied to each end of the string affects the efficiency of the string. The chamber then just alters the tonality and directionality of the tone. This means an electric guitar is not as loud as an acoustic not because of the chamber, but the material used for the strings and body.

If you can recommend a technical and precise book on acoustics that deals with the matter, that would be very helpful.

• If you bolted the violin strings to the wall and drew them over a bridge that was mounted to the wall, then the wall would probably do a fine job of amplifying the sound. If you put a wall "in front of" the violin, then very little energy is coupled into the wall; most is reflected off. Commented Nov 7, 2014 at 4:16
• A good answer to this question would explain how the sound chamber in a musical instrument is an impedance matcher between the string and the air. Commented Nov 7, 2014 at 6:43

## 2 Answers

Resonance occurs when small amounts of energy accumulate because the rate at which they are being added matches the the frequency of the system itself and the phase. The classic example is pushing a child on a swing. If you add energy, ie push, at a frequency that matches the fundamental frequency of the pendulum motion of the swing the amplitude slowly increases. The phase also matters because for optimum energy transfer from you to the swing you need to add it at the correct phase ie at the end points of the cycle.

So if you want to (apparently) amplify a particular frequency of sound you need to put it in a chamber where that frequency is also the resonant frequency of the chamber (or a multiple thereof - think pushing the swing 1 in every every 2 or 3 swings etc).

• Yes I understand this, but I don't understand how what you described can make a sound source more efficient. Frequency response of a wall or any passive object can be spiky or in other words "resonant", but it will never make a sound louder. So what is the mechanism which makes the sound production process more efficient?
– Tony
Commented Nov 7, 2014 at 16:54
• Double post. But to explain more, I am stuck thinking that if you put objects near a sound source it should dampen the source, since pretty much everything is going to absorb more power than air. This is obviously wrong, but I don't understand where I am making the error.
– Tony
Commented Nov 7, 2014 at 16:54
• Most hard surface reflect sound very well. You just get a buildup of sound at the resonant frequency of the cavity, until the rate of input equals the rate at which the sound being absorbed.
– user56903
Commented Nov 7, 2014 at 20:02

Try to get your hands on the book "The Physics of Musical Instruments" By Fletcher and Rossing. All those issues are well discussed there; many physicists have digged on those subjects.

Short summary for your questions: Violins and guitar bodies use a vast array of tricks to amplify the sound. A vibrating string, by itself, radiates as sound only a small part of the energy; the most part is wasted, so a string alone has a feeble sound.

The violin body couples to string vibration, extract energy from it and efficiently transform it in vibration of the air (sound). We all call it "amplification" altough is not strictly correct, since no extra energy is injected.

The top plate (soundboard) vibrates directly under the string pressure; being it large and flat, it moves a lot of air and produces a lot of sound. The sound board must be flat, light and flexible to do that.

The resonance chamber does several jobs, one of wich is to transfrom the small vibrations of the violin body into in-out motion of the air through the sound holes, that again increase sound radiation efficiency. It also suppress destructive self-interference of body surfaces. It must be "of the right size & shape" for the frequencies involved, and have some coupling to the sound source.

Playing with those effects you have all resonancies (vibration modes) of the body and cavity, that affect the response (amplification) at each string frequency.