Check out this table I compiled with note wavelength and directivity. Please note this is specific to only one cello tested.
I made this super handy chart to show the directionality and cycle length of all chromatic frequencies on the cello. (So this won’t have quarter or 3/4 tones… and if you’re here for that, congrats to you for being an even bigger nerd than me). What does all of this mean?
Characteristic to the violin and the viola, the overall directivity of the cello has two noticeable frequency bands of pronounced radiation. First, below 300 Hz (approx D4), the sound pressure level is above −6 dB in all directions. At the 315Hz (approx. D#4) one-third octave band, most of the sound is directed to both sides and the bottom. Second, at the 1250 Hz (D#6 aka Stratosphere) :P one-third octave band, the sound radiation is concentrated to the front and above.
With different dynamics the overall directivity does not present any considerable change. Above 1 kHz more sound is radiated in the top-left direction and the sound pressure levels above 2 kHz are generally increased with higher dynamics, as expected. Meyer (author of one of only a couple major anechoically-isolated studies of stringed instrument acoustics to date) has reported omnidirectional radiation below 200 Hz, which is lower than others. Although I have never tested my own cello in a clinical setting, I have found this to be more true for myself. My own cellos are both 7/8, the finer of the two being even more petite. I find that the omnidirectional range is lower, with some really pronounced pressure around 151 cycle range (approx E3).
The radiation from pronounced plate resonances around 250 – 300 Hz described by Meyer show that radiation is concentrated to both sides at 250 – 315 Hz especially in the bottom elevation. So what does that mean for cellists? I think it’s essential when budget and time permits to make sure you’re playing on an isolated, sound-treated surface.
Meyer found front-directionality at 500 Hz and 2000 Hz (this includes resonant harmonics for frequencies whose fundamental is below this range, a really obvi example of this is bow hiss.) The front-back ratio is cited to first exceed 10 dB at around 500 Hz, which corresponds roughly to the 400–500 Hz observed in other studies.
So, in other words, and something you already know, every cello is different. I hope though that the reader takes away from this that the directionality reallllllyyyy matters when capturing live audio on cello. A good half of my income is derived from re-recording audio that other cellists didn’t quite get right, and it doesn’t have to be that way.
Source: Jukka Pättynen and Tapio Lokki from the Helsinki University of Technology, for their publication, “Directivities of Symphony Orchestra Instruments”. Much of this article was abridged from their anechoic study. Leave it to Fins to give us a thorough study of acoustics. (Kiitos, Suomi)