Atraveling wave is described by the following function y=0.12 cos (4x +2t). here y(x, t) is the displacement of the particle at location x at time t. all quantities are in si units. determine the speed and the direction of the wave.
a. 2 m/s along+x direction.
b. 0.5 m/s along +x direction.
c. 2 m/s along -x direction.
d. 0.5 m/s along - direction.
e. 2 m/s along +y direction.
f. 0.5 m/s along -y direction.

d. 0.5 m/s along -x direction

Explanation:

Wave: A wave is a disturbance, that travels through a medium and transfers energy from one point to another, without causing any permanent displacement of the medium itself.

The general equation of a traveling wave can be expressed as

y = Acos(2πft-2πx/λ) Equation 1

Where A = amplitude of the wave, f = frequency of the wave, λ = wavelength of the wave, x = linear distance, t = time, π = pie.

From the question,

the equation of the moving wave is

y = 0.12cos(4x+2t) equation 2

Comparing equation 1 and 2

-2πx/λ = 4x

λ  = -2π/4

λ  = -2(3.14)/4

λ  = -1.57 m.

Also,

2πft = 2t

f = 2t/2πft

f = 1/π

f = 1/3.14

f = 0.3185 Hz.

Recall that

v = λf Equation 3

Substitute the value of f and λ  into equation 3

v = -1.57(0.3185)

v = - 0.5 m/s.

Note: v is negative because - x direction

Hence the right option is d. 0.5 m/s along -x direction

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2

the following is queen elizabeth’s purposes:

- to encourage the parliament that the technique of picking successors to the seat based merely on birthright needs to be reviewed.

- (not) to convince the parliament that her kid should not be measured as a likely choice for heir to the english power.

- to persuade the parliament that merely since she has a child does not assure that the kid will be a capable leader.

- to sway the parliament how shattering it could be if they proceeded discourteously concerning her or her child.