Acertain transverse wave is described by y(x, t)=bcos[2π(xl−tτ)],where b = 6.40 mm , l = 26.0 cm , and τ = 3.90×10^−2 s .a. determine the wave's amplitude. b. determine the wave's wavelength. c. determine the wave's frequency. d. determine the wave's speed of propagation. e. determine the wave's direction of propagation.

Answer

given,

B = 6.40 mm ,  L = 26 cm ,    τ = 3.90 × 10⁻² s

general wave equation

  y = A cos (k x - ωt)

where A is the amplitude of the

a) Amplitude of the given wave

      B = 6.40 mm

b) Wavelength of the given wave

       λ = L

       λ = 26 cm

c)  wave frequency

            f = 25.64 Hz

d) speed of wave will be equal to

     v = f λ

     v = 25.64 x 0.26

     v = 6.67 m/s

e) direction of propagation will be along +ve x direction because sign of k x and ωt is same as general equation.

area of focus

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.