Respuesta :
Answer:
waves i and iv have the same speed
Explanation:
The speed of a traveling wave the speed of the wave is given by
v = λ f
There is also the speed of oscillation of the particle given by
v_osc = dy / dt
The wave equation has the form
y = A sin (kx –wt)
Let's look for wavelength and frequency
k = 2π /λ
λ = 2π / k
w = 2π f
f = w / 2π
We substitute in the wave speed equation
v = 2π /k w/ 2π
v = w / k
Let's look for the speed in each wave
i) y = 0.12 cos (3x + 2t)
k = 3 m-1
w = 2 rad / s
Let's use the trigonometric relationship
cos (α -π/2) = cos α cos π/2 + sin α sin π/2
cos(α -π/2) = sin α
y = 0.12 sin ( 3x + 2t - π/2)
v₁ = 2/3
v₁ = 0.667 m / s
ii) y = 0.15 sin (6x-3t)
v₂ = 3/6
v₂ = 0.5 m / s
iii) y = 0.23 cos (3x + 6t)
y= 0.23 sin(3x +6t -π/2)
v₃ = -6 / 3
v₃ = -2 m / s
iv) y = -0.29 sin (1.5x-t)
v₄ = 1 / 1.5
v₄ = 0.667 m / s
From these results we see that waves i and iv have the same speed, but differentiate range of motion
