Fan Blade Reflection of Sound
I play guitar. But I have noticed that in the summer
when it gets really hot, and i turn on the ceiling fan, my guitar
sound is "choppy." The first thing that I thought about was the
ceiling fan blades interfering with the sound waves bouncing back to
my ears. But I noticed that this only happens with the higher pitched
strings. I thought that maybe it did not happen with the lower pitched
strings because of their lower frequency, but it is still not making
any sense to me. Why do the higher pitched strings sound more "choppy"
than the lower ones?
The lower-pitched sound waves have wavelengths much larger than the
distance between the fan blades and the ceiling. The total path length
from guitar to fan blade to ear is shorter than the path from guitar to
ceiling to ear. For low-frequency sound, the path difference is small
compared to the wavelength, so the phases of the two waves are not very
different, and their interference does not produce a noticeable change.
For certain frequencies of sound, the path difference will be exactly
equal to some number of wavelengths, and these frequencies should not
sound choppy either. For example, the fifth fret of your high E string
produces sound at a frequency of 440 Hz (wavelength 330/440 = .75 m,
where '330' is the speed of sound in m/s). If the distance between
the fan blades and the ceiling happens to be half of this wavelength, or
roughly one foot, then this frequency should not sound as choppy as
other nearby notes. So if you were stuck on a desert island with only
a guitar, a ceiling, and a fan, and you wanted to know the distance
between the fan blades and the ceiling, you could measure it by noticing
which notes sound choppy.
Good observation, Henry.
This makes sense to me.
To high-frequency sound waves, smaller than the width of the fan blade,
it looks like a flat obstruction, and efficiently reflects them back at you.
To low frequency sound-waves, longer than the width of the fan blade,
it looks like a stir stick in a slow stream.
The sound pressure wave mostly flows around it and keeps on going.
The speed of sound in air is about 340meters/sec.
Presuming your fan-blade is 4 inches wide (10cm, 0.1 meter),
the transition frequency will be (340 meter/sec) / (0.1 meter) = 3400
So indeed, only the highest overtones of your strings will reflect back to
your ears when a blade passes by.
This kind of distinction happens in radio waves and water-waves, too.
You have impressive powers of observation!
For a wave to be affected in a major way by an obstruction, the wavelength
of the wave must be comparable to or smaller than the size of the
obstruction. For example, a large ocean wave would barely notice a narrow
post or a buoy in its path. However, a breakwater whose size is comparable
or larger than the wavelength of the wave can modify the wave drastically,
absorbing or reflecting it.
The fan blades, I assume, are about 1/2 foot in size. A middle C has a
frequency of about 261.1 Hz. So (using wavelength = speed of
wave/frequency and speed of sound in air of 1100 ft/s) middle C produces a
wave with a wavelength of about 4.2 feet. I would expect it to be not much
bothered by the fan. If you go up two octaves, however, the frequency is
quadrupled (it doubles every octave) and the wavelength is a little over 1
ft. I would think it would begin to notice the fan blades. Another octave
or two and it will certainly be strongly affected by the fan blades.
This is a common phenomena. For example, radar used to detect rainfall must
use electromagnetic waves with wavelengths comparable to the size of rain
droplets in order to be reflected by the rain drops.
Best, Dick Plano, Professor of Physics emeritus, Rutgers University
Part of that could be due to the proximity of the fan blades to the ceiling.
at 60 hz, one full length of a sound wave is about 18 feet long. at 400
hz, about 2 feet long, and at 2 Khz, a little more than 6 inches long. For
the longer wavelengths, the sound reflecting off of fan blades is not
significantly out of phase with those from the ceiling. The shorter
wavelengths however, have time to get up to 180 degrees out of phase.
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Update: June 2012