Answer: a) v = ω /k, b) v = - ωAcos( kx −ωt)
Explanation:
y(x,t)=Asin(kx−ωt) defines the wave equation.
a)
We are asked to find wave speed (v)
Recall that v = fλ
From the wave equation above,
k = 2π/ λ where k is the wave number and λ is the wavelength, λ = 2π /k
ω = 2πf where f is the frequency and ω is the angular frequency.
f = ω/ 2π.
By substituting for λ and ω into the wave speed formulae, we have that
v =( ω/ 2π) × (2π /k)
v = ω/k
b)
y(x,t)=Asin(kx−ωt)
The first derivative of y with respect to x give the velocity (vy)
By using chain rule, we have that
v = dy/dt = A cos( kx −ωt) × (−ω)
v = - ωAcos( kx −ωt)
consider the forces on mass m₁ on the incline plane :
parallel to incline , force equation is given as
T - m₁ g Sin30 = m₁ a
T = m₁ g Sin30 + m₁ a eq-1
consider the force on mass m₂ on the incline plane :
m₂ g - T = m₂ a
T = m₂ g - m₂ a eq-2
Using eq-1 and eq-2
m₂ g - m₂ a = m₁ g Sin30 + m₁ a
inserting the values
(2.3 x 9.8) - 2.3 a = (3.7 x 9.8) Sin30 + 3.7 a
a = 0.74 m/s²
Answer:
Gamma rays occupy the short-wavelength end of the spectrum; they can have wavelengths smaller than the nucleus of an atom. Visible light wavesare one-thousandths the width of human hair--about a million times longer than gamma rays. Radio waves, at the long-wavelength end of the spectrum, can be many meters long.
