Wave motion is characterized by two velocities: the velocity with which the wave moves in the medium (e. g., air or a string) and the velocity of the medium (the air or the string itself). Consider a transverse wave traveling in a string. The mathematical form of the wave is y(x, t)=Asin(kx−ωt).

a)Find the velocity of propagation v_p of this wave.

Express the velocity of propagation in terms of some or all of the variables A, k, and omega.

b)Find the y velocity v_y(x, t) of a point on the string as a function of x and t.

Express the y velocity in terms of omega, A, k, x, and t.

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)

in simple terms, the principle states that the buoyancy force on an object is equal to the weight of the fluid displaced by the object, or the density of the fluid multiplied by the submerged volume times the gravitational acceleration, g. this is also known as upthrust.

which piece of furniture will have the most inertia and give the furniture movers the most difficulty in moving?  

answer

a 75kg dining table