Editing Longitudinal wave (section)

=== Attenuation in viscoelastic materials ===
In [[viscoelastic]] materials, the attenuation coefficients per length  <math>\ \alpha_\ell\ </math> for longitudinal waves and <math>\ \alpha_T\ </math> for transverse waves must satisfy the following ratio:

:<math>\ \frac{~\ \alpha_\ell\ }{~\ \alpha_T\ } ~\geq~ \frac{~ 4\ c_T^3\ }{~ 3\ c_\ell^3\ }\ </math>

where <math>\ c_T\ </math> and <math>\ c_\ell\ </math> are the transverse and longitudinal wave speeds respectively.<ref>
{{cite journal
 |last=Norris |first=Andrew N.
 |year=2017
 |title=An inequality for longitudinal and transverse wave attenuation coefficients
 |journal=The Journal of the Acoustical Society of America
 |volume=141  |issue=1  |pages=475–479
 |doi=10.1121/1.4974152  |pmid=28147617  |issn=0001-4966
 |arxiv=1605.04326   |bibcode=2017ASAJ..141..475N
 |url=https://pubs.aip.org/jasa/article/141/1/475/1058243/An-inequality-for-longitudinal-and-transverse-wave
 |via=pubs.aip.org/jasa  |lang=en
}}
</ref>