The amplitude of continuous vibrations of the point of the string is 1mm, the frequency is 400Hz.

The amplitude of continuous vibrations of the point of the string is 1mm, the frequency is 400Hz. How long does a string point travel in 0.1 s?

Given:
Continuous vibration;
Amplitude = 1 mm;
Frequency = 400 Hz;
Time = 0.1 s;
Find: path;

Solution:
s = 4 * xm, where xm is the amplitude of the oscillations – this is the path that a point travels in one oscillation;
Let’s find the number of oscillations in time = 0, 1 s, that is, we get: N = t / T = t * v, where v is the oscillation frequency.
The path that the point of the string will pass is: s = N * s1 = 4 * xm * t * v = 4 * 1 mm * 0.2 s * 1000 Hz = 4 * 0.001 m * 0.2 s * 1000 Hz = 0.8 m.