Harmonic waves and waves in a cord
Summary ratings: 3 stars
(xx voters)
Autor streszczenia
:
Essay
Wizyty:
57
słów:
600
Opublikowano dnia: stycznia 09, 2008
The sine or harmonic wave propagates fulfilling with the equation: y=A.sen (kx-wt+f), where A is the amplitude of the wave, w corresponds to the angular velocity (w=2pi.f) and k denominates the wave´s number (k=2pi/longitud of wave). The angular velocity indicates that the phenomenon is repeated in the time and k represents the space repetition of the propagation. Magnitude f is the initial phase and indicates that the undulatory phenomenon has already propagated before the moment for having begun the measuring of the times. As departure point we consider a cord in its stable state, put under a tension T, and with a linear density of constant mass m (mass by length unit). The characteristics of the propagation’s speed of the transversal waves in the cord are summed up in the equation: v= (T/m) ½. That is to say, when the tension increases the waves in the cord travels more quickly; the same happens if the density of mass is diminished (rope “thinner”). For example, the second cord of a guitar tunes to the note, the one that corresponds to a frequency of 440 Hertz; supposing that the chord length is of 90 cm, and the linear density of mass of 10-3 kg/m, and the tension is of 627 N, approximately. If the tension is diminished the vibration’s frequency generated would be smaller than 440 Hertz, whereas if the tension is increased the frequency would be superior.
On the other hand, the first cord has a linear greater density of mass, reason why if it is subject to the same tension that the second, the frequency of the vibration generated is smaller than 440 Hertz; whereas the third to sixth cords have minors linear densities of mass that the second, reason why the frequencies of the vibrations generated are superior, if they are put under the same tension.