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 <mailto:[EMAIL PROTECTED]>
To: U.S. Metric Association <mailto:[email protected]>
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.
