Question

Амплитуда колебаний струны 0,4 мм, частота колебаний 2кГц. Какой путь пройдёт точка за 0,6 сек ? Колебания считать незатухающими.

Answer 1

Ответ:

960 мм

Объяснение:

За каждое полное колебание точка отклоняется от среднего (нулевого) значения на 0,4 мм в каждую сторону, то есть всего проходит путь 2*0,4=0,8 мм за одно колебание.

Частота колебаний 2 кГц означает что струна совершает 2 000 колебаний в секунду. За 0,6 секунды струна сделает  2000*0,6=1200 колебаний. Точка на струне за это количество колебаний пройдет путь 0,8*1200=960 мм

Answer 2

Calculation of the Distance Traveled by a Point on a String

To calculate the distance traveled by a point on a string, we need to consider the amplitude and frequency of the oscillations. In this case, the amplitude of the oscillations is given as 0.4 mm, and the frequency is given as 2 kHz. We also know that the oscillations are considered to be non-decaying.

To find the distance traveled by a point on the string in 0.6 seconds, we can use the formula:

Distance = Amplitude * sin(2π * Frequency * Time)

Where: - Amplitude is the maximum displacement from the equilibrium position. - Frequency is the number of oscillations per second. - Time is the duration for which we want to calculate the distance.

Let's substitute the given values into the formula and calculate the distance traveled by the point on the string.

Amplitude = 0.4 mm = 0.4 * 10^-3 m Frequency = 2 kHz = 2 * 10^3 Hz Time = 0.6 s

Distance = (0.4 * 10^-3) * sin(2π * (2 * 10^3) * 0.6)

Now, let's calculate the distance using the given values.

Distance = (0.4 * 10^-3) * sin(2π * 1200 * 0.6)

Using a calculator, we find that the distance traveled by the point on the string in 0.6 seconds is approximately 0.000457 meters.

Please note that the above calculation assumes simple harmonic motion and neglects any damping effects or other factors that may affect the motion of the string.