Chapter
4 - Resonance |
Frequency
and Associated Harmonics |
Questions
to Consider |
|
On page 57, in the book, the author confuses the issue of Nodes and Anti-nodes. The author even states this in the second paragraph. Nodes occur at minimum displacement of the medium. The author mixes pressure nodes with displacement nodes. It's all so confusing. Transverse waves (strings) are different than Longitudinal waves (sound). Transverse waves are easily represented by sine and cosine waves. Longitudinal waves are NOT easily represented by sine and cosine waves. Enough said. |
Guitar Example |
Consider
a 80-cm long guitar string which has a fundamental
frequency (1st harmonic) of 400 Hz. For the first harmonic, the
wavelength of the wave pattern would be two times the length of the string;
thus, the wavelength is 160 cm or 1.60 m. The speed of the standing wave
can now be determined from the wavelength and the frequency. The speed of
the standing wave is |
speed = frequency * wavelength
speed = 400 Hz * 1.6 m speed = 640 m/s |
This speed
of 640 m/s corresponds to the speed of any wave within the guitar
string. Since the speed of any wave is dependent upon the properties
of the medium (and not upon the properties of the wave), every wave
will have the same speed in this string regardless of its frequency and
its wavelength. So the standing wave pattern associated with the second
harmonic, third harmonic, fourth harmonic, etc. will also have this speed
of 640 m/s. A change in frequency or wavelength will NOT cause a change
in speed. |
Sympathetic Vibrations System A vibrations caused by System B vibrating at the same resonant frequency of System A. Example: If you bring a vibrating tuning fork near a piano string board then one string that resonates at the frequency of the tuning fork will begin to vibrate. It's a cool experiment. |
After
all this time, I have asked you all about the frequency of the C note
on the piano. Have you discovered this, yet? Maybe, it would be worth
your time to understand this setup.Look
here.
|