  The source of the hummingbirds distinctive hum is not well understood, but
there are clues to its origin in the acoustic nearfield and farfield. To
unravel this mystery, we recorded the acoustic nearfield generated by six
freely hovering Annas hummingbirds using a 2176 microphone array. We also
directly measured the 3D aerodynamic forces generated by the hummingbird in
vivo using a new aerodynamic force platform. To determine the degree to which
the aerodynamic forces cause the hum, we developed a simple first-principles
model to predict the acoustic field radiated by the 3D oscillating forces. The
correspondence between the predicted and measured acoustic field shows the
primary acoustic sources of the hum are the lift and drag forces that oscillate
as the flapping wings move back and forth. The model also shows how the
aerodynamic force profile of the flapping wing determines the hums timbre and
sound pressure level: profiles that support bodyweight with higher harmonics
radiate more acoustic power. Further, extending this model across birds and
flying insects, we show how the radiated acoustic power scales with body mass
to the second power - with allometric deviation making larger birds quieter and
elongated flies louder. The model's ability to predict the acoustic signature
of flapping wings suggests it can be applied for such diverse uses as
differentiating wing and feather sounds in bird display behaviors to
interpreting how insects generate courtship songs with their wings to making
flapping robot wings more silent.
