Male Rocky Mountain elk (Cervus elaphus nelsoni) produce loud and high fundamental frequency bugles during the mating season, in contrast to the male European Red Deer (Cervus elaphus scoticus) who produces loud and low fundamental frequency roaring calls. A critical step in understanding vocal communication is to relate sound complexity to anatomy and physiology in a causal manner. Experimentation at the sound source, often difficult in vivo in mammals, is simulated here by a finite element model of the larynx and a wave propagation model of the vocal tract, both based on the morphology and biomechanics of the elk. The model can produce a wide range of fundamental frequencies. Low fundamental frequencies require low vocal fold strain, but large lung pressure and large glottal flow if sound intensity level is to exceed 70 dB at 10 m distance. A high-frequency bugle requires both large muscular effort (to strain the vocal ligament) and high lung pressure (to overcome phonation threshold pressure), but at least 10 dB more intensity level can be achieved. Glottal efficiency, the ration of radiated sound power to aerodynamic power at the glottis, is higher in elk, suggesting an advantage of high-pitched signaling. This advantage is based on two aspects, first, the lower airflow required for aerodynamic power and, second, an acoustic radiation advantage at higher frequencies. Both signal types are used by the respective males during the mating season and probably serve as honest signals. The two signal types relate differently to physical qualities of the sender. The low-frequency sound (Red Deer call) relates to overall body size via a strong relationship between acoustic parameters and the size of vocal organs and body size. The high-frequency bugle may signal muscular strength and endurance, via a vocalizing at the edge mechanism, for which efficiency is critical.