During the heightened sexual and aggressive period of musth, males produce a distinctive rumble with a characteristically pulsated "put-put-put" or "glug-glug-glug" quality, like water gurgling through a deep tunnel. This is known as a musth-rumble and it is associated with an increased rate of Urine-Dribbling and a particular ear posture known as an Ear-Wave.
Males tend to give musth-rumbles in rather specific contexts such as during aggressive interactions with other males, when they approach a group of females, when they are marking a tree with Temporal-Gland-Secretion, drinking, or wallowing, as well as in situations where they feel challenged.
For example, the sound of another musth male, an approaching vehicle or even an airplane overhead is often enough to trigger a musth male to rumble. Musth males also frequently rumble before or after listening, when they are presumably responding to distant elephant calls or using calling to search for potential mates.
Example: Musth-rumble by RBG
Musth males most often rumble when they are alone, less often in the company of females and least often when they are guarding an estrous female. Since musth males often listen after they rumble, it's likely that they use musth-rumbles to advertise their heightened aggressive and sexual state to rival males and to potential mates. Females respond to the rumbles of musth males by vocalizing, so calling may help a male to locate groups of females. Once a male has located an estrous female he may have neither the need nor the desire to advertise his whereabouts!
The calls of individual males are distinctive. Some males produce short musth-rumbles, others are very long, some are rolling while others are highly pulsated. The "typical" musth-rumble is a long, low, pulsated, tonal call with considerable overlaying noise.
Multimedia Resources 
ElephantVoices Gestures Database
ElephantVoices Photo Database
ElephantVoices Video Database
ElephantVoices Calls Database