They say a Moluccan cockatoo's screech has a decibel level of around 129 or even more (e.g., 135). That is almost as loud as a jet engine (140 dB at 100 feet).
How are they able to emit a screech that loud? Don't they hurt themselves?
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I don't have a copy of the book so was not able to check the author's sources. However, I can answer a more general question about how birds are able to make loud noises in general.
Birds have a syrinx instead of a larynx as in mammals. This is situated at the bottom of the trachea, instead of at the top. Given this, birds can take advantage of acoustic resonance, which can allow for some extremely loud calls.
In a 21 Oct 2019 article in the New York Times titled "The Loudest Bird in the World Has a Song Like a Pile Driver" (paywall), the South American white bellbird is said to be the loudest bird in the world at 125 dB. (With the screaming piha now in second place). The study, "Extremely loud mating songs at close range in white bellbirds" was conducted by Dr. Jeffrey Podos and Dr. Mario Cohn-Haft in 2018. Unfortunately, it does not seem to cover the biological mechanics that produce such loud calls, but rather focuses on the evolutionary and sexual pressures that have led to such outliers in avian acoustics.
Note that decibels are a measure of acoustic sound pressure, and vary greatly depending on the distance from the source they are measured. In order to be scientifically sound, the loudness of something should be measured from a fixed distance under controlled conditions. Note that the table of examples of sound pressure levels contains a "distance" column, which is extremely important for comparison purposes between sounds. I have no idea whether the parrot measurements were conducted using the same criteria as the white bellbird study (very likely not). Therefore, the higher dB values listed there may be due to measurements with much smaller distances.