Thanks for the in-depth discussion of sounds related too instruments.
Stan Doore
----- Original Message -----
From: J. Ward
To: U.S. Metric Association
Cc: U.S. Metric Association
Sent: Tuesday, January 15, 2008 10:40 PM
Subject: [USMA:40082] Frequency and wavelength
There is a difference that gives frequency a fundamental importance relative
to wavelength, especially for sound. A vibrating string has a specific
fundamental frequency. For that particular string & frequency there is a
well-defined wavelength. The vibrating body of the instrument (piano sound
board, guitar body, etc.) will vibrate at the same frequency as the string, but
**not** at the same wavelength. The wavelength in the sound board may not even
be well defined. The vibrating soundboard then gets air molecules moving,
which will also vibrate at the same frequency as the string and sound board,
but at yet a different wavelength. It is the frequency that stays the same
while the wavelength changes. Furthermore, if you strike a tuning fork, it
rings with a specific frequency which you perceive as a specific pitch (such as
"A" or "La"). Strike the same tuning fork at a different air pressure (such as
at a higher altitude) and it will still have the same frequency, and you will
perceive the same pitch ("A" or "La"). But the wavelength will be different
due to the different air pressure.
Therefore, frequency is a more fundamental property of the propagating waves
than wavelength, and pitch is almost always related to frequency rather than
wavelength. Put another way, just telling the frequency immediately gives the
pitch and allows one to determine the wavelength for any given medium (air,
string, etc.) But telling someone a wavelength for a sound wave is almost
useless if you don't specify the details of what it's propagating in, such as
the composition, temperature and pressure of air, or the tension and mass per
unit length of a string.
JW
STANLEY DOORE wrote:
Each frequency specified in Hertz has a specific wave length. Some
frequencies can be heard by humans while others cannot. There is a direct
relationship between frequency and wave length.
The fundamental frequency of a stretched string or wire is given by:
n = 1/2L (sq route of T/m) where
L = length T = tension m = mass per unit length
Knowing this, electronic pianos and other musical instruments have been
manufactured with good approximation.
Use of frequency and wave length depends on the context/discipline with
whom you are communicating. In radio, frequency is used as the center
frequency of a particular bandwidth spectrum. HD radio uses upper and lower
sidebands in a specific spectrum and may contain data and information different
from what's transmitted on the central frequency. Radars are usually specified
by wave-length. Microwave ovens are a particular type of radar.
Stan Doore
----- Original Message -----
From: Bill Hooper
To: U.S. Metric Association
Sent: Monday, January 14, 2008 9:40 PM
Subject: [USMA:40050] Re: Stuart & Sons Pianos
On 2008 Jan 14 , at 5:50 AM, STANLEY DOORE wrote:
Pianos make sound. Sound waves and frequencies (radio and TV) are
given in metric (mm, cm and m) as common practice for more than 100 years. So
it seems logical to build pianos using metric units.
The frequencies of sound waves are not usually "given in ... mm, cm and
m". Those length units could be used to report the wavelength of a wave and
that would be quite correct. However, sound waves are NOT USUALLY reported as
such. Instead, sound waves are almost always specified by their frequency
(which is related to their pitch). Frequency in metric is measured in hertz
(Hz) and its multiples. (One hertz equals one oscillation per second.)
However, many radio/TV waves are also specified by their frequency (in
hertz). While it is true that some of the lower frequency (and therefore
greater length) radio waves have been commonly specified by their wavelength
("millimetre waves", "microwaves*", "3 m waves", "quarter wave length
antennas", etc.) by far, the commercial broadcast bands are almost always
referred to by frequency**.
So, Stanley's suggestion may be good if applied to frequencies in hertz,
but not in connection with wavelengths in millimetres etc.
Regards,
Bill Hooper
==================================
Additional comments, off the main subject but maybe interesting to some.
* I believe "microwaves" is a term used to describe radio waves of
wavelengths in the micrometre range, but I am not certain of that fact. Does
anyone know the wavelength used in common microwave ovens? Such ovens all use
the same frequency, I believe; namely, the frequency which most efficiently
transfers energy to the hydrogen-oxygen bond in water and other molecules.
That's why they heat the water in a cup but not the cup.
**The AM radio band runs from about 550 kHz to 1600 kHz while the FM band
runs from 87.7 MHz to 107.9 MHz. That means the FM waves at the SLOW end of the
FM dial are oscillating about 55 times FASTER than the FASTEST waves on the AM
dial. (87.7 MHz is about 55 times 1600 kHz.) For comparison, audible sound
waves (those that can be heard by the human ear) are in the
range from 20 Hz to 20 000 Hz (20 kHz). These are not sharply defined
because they depends on an individual's ears. I mysefl haven't been able to
hear above 15 kHz most of my life.
