"Mutes reduce the volume of an instrument - no Helmholtz effect"

Ahhh --- lies to children ... :-)


Mutes do not, with the exception of such as drums just reduce the volume by just absorbing energy (but then are lots of things happening there too) ... they primarily interfere with the composition of the partial overtones which primarily causes a perceived change in timbre (and thus perceived volume) - absorption of some energy in the process also causes a perceived lowering of volume.

Mutes on string instruments work by increasing the mass of the bridge, altering the partial overtones transmitted, and thus the timbre. Mutes on wind instruments can either fit inside the instrument - reducing the volume of vibrating air which alters the partials, or be fitted externally, which also affects the volume of the vibrating air - some trumpets will alter timbre when just directed towards the orchestral music stand! This is because the effective volume of the vibrating air which extends beyond the end (end effect) is effectively limited (changed in volume!).

Helmholtz effects occur massively in musical instruments, even guitars.... :-)

... and they occur widely in all sorts of areas of life - a partly would down car window sets the car inside resonating - Helmholtz! Things like exhausts, and air intakes once were thought to resonate only on the tubular length, now it is understood that HR volume effects are critical too!

... from recent research ... our understanding of things change as more research is done - just reading a book published a century ago will likely just mislead one unless one knows that ideas change with time and research ...

QUOTE
A Helmholtz resonator, consisting of a resonating cavity with an open neck, was filled with spheres to determine the effects on the resonant frequency. A function generator and speaker were used to excite the resonator, and Fourier analysis was used to find the resonant frequency. Two sizes of marbles, glass beads, and water were used separately to fill the resonator. Frequency measurements were made at a wide range of open volumes by filling the resonator with different amounts of spheres. The volume of the spheres and the distance from the top of the resonator to the top of the spheres were measured as well. Comparisons of the resonant frequencies of spheres and water at the same height were investigated. It was found that the resonant frequency for water was much higher than the resonant frequency for spheres at the same height, indicating that the air pockets in between the spheres are having an effect on the resonant frequency. In addition, the change in frequency as a function of open volume for both the water and the spheres was studied. A peak in the resonant frequency for the spheres was observed at a certain critical open volume, approximately half of the total volume of the resonator. This effect is contrary to the theoretical dependence of frequency on open volume. The most likely explanation is that a correction is needed in the theory, as the simplest case no longer holds.
UNQUOTE

Life keeps changing on us ...