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Консультация № 138277
28.05.2008, 13:40
0.00 руб.
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Здраствуйте, необходимо решить задачу из раздела Колебания:
Источник с частотой 1000 Гц и амплитудой 0,5 мм возбуждает в упругом шнуре волну длиной 0,35 м. Найти скорость распространения колебаний и максимальную скорость колеблющихся точек шнура.
С уважение, Дмитрий.
Приложение:
К решению задаче, также нужен рисунок.
Источник с частотой 1000 Гц и амплитудой 0,5 мм возбуждает в упругом шнуре волну длиной 0,35 м. Найти скорость распространения колебаний и максимальную скорость колеблющихся точек шнура.
С уважение, Дмитрий.
Приложение:
К решению задаче, также нужен рисунок.
Обсуждение
Неизвестный
28.05.2008, 14:55
общий
это ответ
Здравствуйте, Быковский Дима Генадьевич !
Связь длины волны λ=0,35 м с её частотой n=1000 Гц и скоростью распространения V:
V=λ*n=0,35*1000=350 м/с
Чтобы найти максимальную скорость колеблющихся точек шнура, запишем уравнение колебаний, предполагая, что источник дает гармонические колебания:
x=A*cos(ω*t) (1)
где А=0,5 мм=0,5*10<sup>-3</sup> м - амплитуда колебаний, ω - угловая частота, которая связана с частотой n через множитель 2*pi:
ω=2*pi*n (2)
Скорость U колебания точек - первая производная от координаты, продифференцируем (1):
U=-ω*A*sin(ω*t) (3)
Поскольку sin(ω*t)<=1, максимальное значение скорости по модулю равно:
U=ω*A=2*pi*n*A=2*3,14*1000*0,5*10<sup>-3</sup>=3,14 м/с
Извините, что нет рисунка, но особого смысла я в нем здесь не вижу
Связь длины волны λ=0,35 м с её частотой n=1000 Гц и скоростью распространения V:
V=λ*n=0,35*1000=350 м/с
Чтобы найти максимальную скорость колеблющихся точек шнура, запишем уравнение колебаний, предполагая, что источник дает гармонические колебания:
x=A*cos(ω*t) (1)
где А=0,5 мм=0,5*10<sup>-3</sup> м - амплитуда колебаний, ω - угловая частота, которая связана с частотой n через множитель 2*pi:
ω=2*pi*n (2)
Скорость U колебания точек - первая производная от координаты, продифференцируем (1):
U=-ω*A*sin(ω*t) (3)
Поскольку sin(ω*t)<=1, максимальное значение скорости по модулю равно:
U=ω*A=2*pi*n*A=2*3,14*1000*0,5*10<sup>-3</sup>=3,14 м/с
Извините, что нет рисунка, но особого смысла я в нем здесь не вижу
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