For one thing, they emit a sound louder than that of any other living creature. They use a specialised cavity in their heads to focus and reflect a loud 'click' which is generated by an organ known as the 'monkey lips'. This click can be as loud as 200dB which is thousands of times louder than the volume that would cause pain to us humans and can be heard from 60km (40 miles) away. So loud are these sounds that in the days of sail, people would hear them from inside their ships and compare their sound to that of someone hammering a nail into wood. Hence the term 'carpenter fish' was in common use long before people realised that the sounds were made by sperm whales - not fish at all.
These sounds are not like the the beautiful songs of the humpbacks. They are clicks of varying frequency used like sonar to locate and hunt their prey - giant squid. As the whale nears it victim the frequency of the clicks increases to improve the whale's accuracy in locating its meal.
More on the Acoustic World of the Sperm Whale can be found here.
Of course the long and intractable story of Moby Dick by Herman Melville describes one man's obsession with a sperm whale. I found it very difficult to reach the end of that book, but was much more fascinated by a factual book about the true-life version of Captain Ahab. 'In the Heart of the Sea' by Nathaniel Philbrick made the story much more readable. The first half of the book about the Whaleship Essex described the technology of whaling in a fascinating way. It revealed how the island of Nantucket relied on whaling to support itself, and how the island was governed to nurture their industry. The second half was more harrowing but also educational as it described the privations of the men who had to attempt to survive in an open boat in the middle of the Pacific Ocean.
I should say that I am not in favour of commercial whaling. At least in the time of Captain Ahab the whale had a bit more of a sporting chance than in these days of mechanised slaughter.
The substance 'ambergris' (also known as 'floating gold') comes from sperm whales too. It is the residue of the beaks of squid, and for some reason it accumulates into hard lumps with a musty aroma.
It is surprising that the world's most expensive perfumes contain something from a sperm whale's rectum, but it appears that this substance has an amazing ability to retain a fragrance.
How on earth did anyone discover that?
Related post: Stop the Bloody Whaling