If a guitar string has a fundamental frequency of 500 Hz, which one of the following frequencies can set the string into resonant vibration? a. 250 Hz
b. 1500 Hz
c. 1750 Hz
d. 750 Hz

The frequency that can set the string into resonant vibration is 1,500 Hz.

Explanation:

Given;

fundamental frequency of the string, F₀ = 500 Hz

The frequencies that can set the string into resonant vibration must be higher frequencies, such frequencies include the first overtone, second overtone, third overtone, etc.

The first overtone, F₁ = 2F₀ = 2 x 500 = 1,000 Hz

The second overtone, F₂ = 3F₀ = 3 x 500 = 1,500 Hz

The third overtone, F₃ = 4F₀ = 4 x 500 = 2,000 Hz

Therefore, the frequency that can set the string into resonant vibration is 1,500 Hz.

its a 5.5 n

glad that

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.