Sound amplification by stimulated emission of radiation implies that lasers should be as feasible with sound as they are with light. In the 21st century, it is easy to produce low frequency sound in the range that humans can hear (~20 kHz), in either a random or orderly form. However, at the terahertz frequencies in the regime of phonon laser applications, more difficulties arise. The problem stems from the fact that sound travels much slower than light. This means that the wavelength of sound is much shorter than light at a given frequency. Instead of resulting in orderly, coherent phonon laser structures that can produce terahertz sound,
Stimulated emission an atomic or molecular resonance, the spectral line shape function is described as a Lorentzian distribution where formula_12 is the full width at half maximum or FWHM bandwidth. The peak value of the Lorentzian line shape occurs at the line center, formula_13. A line shape function can be normalized so that its value at formula_9 is unity; in the case of a Lorentzian we obtain Thus stimulated emission at frequencies away from formula_9 is reduced by this factor. In practice there may also be broadening of the line shape due to inhomogeneous broadening, most notably due to the Doppler effect