"Bowhead," a picture of a sound made by a Bowhead whale, 2003 by Mark Fischer (using wavelet analysis of recorded hydrophone sound data)
Artist Mark Fischer was interested in whalesong and found that in the literature you could find information on the range of frequencies employed, or fourier transforms of recorded sound (so you could see it plotted as a function of frequency, or moreorless which 'notes' were used, if whales happened to use discrete notes like most human music). He decided to use a method common in my field - marine geophysics. He employed wavelet analysis. (If you're interested, this is something seismologists typically use. They take time series data, which means they measure the amplitudes of vibrations, which is often equivalent to measuring the intensity of sound, periodically, so they get a series of measurements in time. They convolve the time series with a wavelet, a specific function. The result is a matrix of numbers which can be displayed as a 2D image if you simply map numbers onto colours.) It suffices to understand that there are a series of numbers (equivalent to the whalesong) to which he applies a mathematical procedure to produce an image. As he writes,
The procedure I have developed to pursue this exploration is, to me, a form of photography- with mathematics as the lens and a computer as a camera. What results is something I call 'the shape of the sound'.
More recently he's produced wavelet images of birdsong and insect noises and what he calls 'AguaSonic' videos of various species, so you can hear the animals too.
Pseudorca Pontinha by Mark Fischer, 2009 17.75" x 23.75" archival digital print on Crane's Museo Max paper
Sound as visual art can also be of sounds closer to the human experience (and not only those which require hydrophones to record). Epic Frequency makes prints of famous audio clips. This one is Martin Luther King, Jr. beginning, "I Have A Dream" On August 28, 1963.
Or, here is a way in which natural sounds combine with sculptural art. 'Hear Heres' is a set of four giant ear trumpet sculptures designed to highlight the sounds of nature, by London architecture firm Studio Weave.