You perform an experiment with a long column of air and a tuning fork. The column of air is defined by a very long vertical plastic tube with a circular cross section; the upper end of the tube is open to the outside air and the lower end of the tube is filled with water. The column of air extends from the top of the water to the open end of the tube; the length of the column can be varied by changing the water level in the lower end of the tube. (The columns of air in this problem are longer than those you will have used in lab; this allows us to imagine the use of lower frequency tuning forks than those you will have used in lab.)
ou are using a tuning fork of frequency 256 Hz. For one particular water level, you hear a loud sound when the fork is struck and positioned just above the open end of the tube. When the water level is lowered by 676 mm, you again hear a loud sound.
(a) What is the wavelength of the 256 Hz sound waves in the column of air? Give your answer in meters, not mm. m
(b) What is the speed of sound in the column of air? m/s

a) The wavelength, λ = 1.352 m

b) The speed of the sound in the column air is v = 346.112 m/s

Explanation:

a) Frequency, f = 256 Hz

The water level is lowered by 676 mm. i.e. x = 676 * 10⁻³ m

The length, x, at which the loudest sound will be heard is λ/2

i.e. x =  λ/2

Therefore the wavelength of the 256 Hz sound waves in the column air is given by the relation

λ = 2x

λ = 2 * 676 * 10⁻³

λ = 1.352 m

b) The speed of the sound in the column air:

The speed, v, is given by the relation   v = f  λ

speed, v = 256 * 1.352

v = 346.112 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s

given:

acceleration = 0.6

time = 4.5 s

to find:

velocity = ?

formula used:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

solution:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

v = 0 + (0.6 × 4.5)

v = 2.7 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s

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.