The “Wavelength” of a Guitar

The acoustical anatomy of a guitar is knowable, but it is complex, dynamic, three-dimensional and invisible to both the eye and ear. By learning and applying various sensory techniques and mental tools, one can learn to build a working mental model of the guitar in a manner that might be called “throwing flour on the invisible man”.

The first and most fundamental mental tool is to learn to view physical objects in terms of their acoustical wavelength and corresponding audible frequency. The dimension of every object or feature corresponds to a particular wavelength of sound, and just as you can see the physical size of an object by just looking at it, with a little practice you can learn to simultaneously “see” its acoustical wavelength and corresponding audible frequency. 

The speed of sound in air is approximately 345 meters/sec, which is a pretty easy number to remember. For the non-metrically inclined, using 1000 ft/sec for the speed of sound will be off by just 10%, which is close enough. To see an object’s frequency you simply divide the speed of sound by the physical dimension of the object. For example, a one-meter object has a wavelength corresponding to a frequency of 345/1 = 345 Hz. A 0.5 meter object will correspond to a frequency of 345/0.5 = 690 Hz, and so on. In the illustration above, the length of a typical guitar corresponds approximately to the wavelength produced by an A-440 tuning fork.

The human audible frequency range is from 20 Hz to 20,000 Hz, if you have taken care of your hearing. The wavelength of the lowest frequency is about 50 ft., roughly the size of a house.

The wavelength of the highest audible frequency is about two-thirds of an inch – roughly the length of a guitar bridge pin.

The reason “seeing” the audible frequency corresponding to an object’s size is so important is that it tells you immediately how sound will interact with that object. Small object features will be invisible to long wavelengths, while large object features will reflect short wavelengths like light. This is precisely why we can hear around corners, but we cannot see around corners.

The wavelength of light is very small, roughly one-one-hundredth of the thickness of a piece of paper. Interestingly, the width of a razor-sharp knife edge is a bit less than the wavelength of light, while the width of a dull knife edge is larger than the wavelength of light. If you hold up and look closely at a knife edge, dull sections will reflect a glint of light like the blade on the right, while the razor-sharp edge on the left cannot reflect light, and is literally invisible.

Now you will go through your knife drawer and compulsively sharpen until all your cutting edges are invisible.