Hi Ricky, and welcome to Permies.
I did a google search for 'sound damping qualities of straw" and came up with these results, which don't surprise me:
Straw Bales as Soundproofing
So the answer to the question is yes. Yes, straw bale buildings are incredible insulators from sound. If you live on a very loud street or perhaps you back to an interstate, these walls will eliminate almost all of the noise that you currently live with. You can build a straw bale house or consider building a straw bale landscape wall. Although not as good as an entire house of straw, they still work really well to eliminate sound.
Acoustical Characterization of Straw Bales as Structural Elements
Straw bale walls, in addition to being highly insulating, inexpensive, and providing minimal impact on the environment, have the ability both to impede and transmission of sound energy and absorb noise over a wide range of frequencies. As architects begin to take advantage of straw's acoustical strengths, straw bales could be used more extensively in building construction and in other applications. For example, this study suggests that straw bale walls would be excellent candidates for use an inexpensive outdoor barriers to reduce environmental noises such as highway noise.
Straw-bale Sound Isolation and Acoustics
The 53dBA test result might seem low but in fact is very good. Most conventional wall systems including a brick cavity wall with much higher mass have a lower performance. Specifically interesting to note is the 2-3dB better performance at very low frequencies of the straw-bale test sample when compared to brick-wall systems. Nearly all wall systems, including stick frame, are able to sufficiently subdue high-and mid-frequency sound, but low-frequency sound is problematic. In practice, better performance at low frequencies is worthwhile because it means that the ever-present background noise in suburban areas is perceptibly reduced.
What
did surprise me is that Google wanted to correct my search to 'sound damp
ening qualities of straw', which would be the ability of straw to get sound wet, I guess.