What is the correct capitalisation of the word "sonar" (and why)?
The Chicago Manual of Style notes (emphasis mine):
Initialisms tend to appear in all capital letters, even when they are not derived from proper nouns (HIV, VP, LCD). With frequent use, however, acronyms—especially those of five or more letters—will sometimes become lowercase (scuba); those that are derived from proper nouns retain an initial capital.
"A Brief History of Active Sonar" (note the capitalization of sonar in title case; the same applies at the start of a sentence) documents that sonar was coined in 1942, following the pattern of radar.
It's instructive to note that the forerunner of the sonar was the ultrasonic ASDIC (Allied Submarine Detection Investigation Committee); asdic is listed as a synonym for sonar in British English.
From the Guardian Style Guide:
abbreviations and acronyms
Use all capitals if an abbreviation is pronounced as the individual letters: BBC, VAT, etc; if it is an acronym (pronounced as a word) spell out with initial capital, eg Nasa, Nato, unless it can be considered to have entered the language as an everyday word, such as awol, laser and, more recently, asbo, pin number and sim card. Note that pdf and plc are lowercase.
So it's "Sonar", since it's an acronym -- or maybe "sonar" if you believe it has become an everyday word.
But the Guardian Style Guide is just one guide. Other publishers may have different guidelines.