The equation for a wave moving along a straight wire is: (1) y= 0.5 sin (6 x - 4t)
To look at the motion of the crest, let y = ym= 0.5 m, thus obtaining an equation with only two variables, namely x and t.

a. For y= 0.5, solve for x to get (2) x(t) then take a (partial) derivative of x(t) to get the rate of change of x which is the velocity of the wave.

A separate wave on the same wire is: (3) y= 0.5 sin (6x + 4t)

b. For y= 0.5, solve for x to get (4) x(t) then take a (partial) derivative of x(t) to get the rate of change of x which is the velocity of the wave.

c. From parts a and b, state how you can tell whether a wave is moving toward +x or toward -x direction.

Solution Preview

a. In a general equation, y= ym sin (kx - wt), if we let y= ym then ym cancels and we get:
sin (kx - wt) = 1 from which kx - wt = Arcsin 1 and x= (w/k)t + (Pi)/(2k)
In ...

Solution Summary

The derivatives of wave equations are determined. A separate wave on the same wire are determined. With good explanations and calculations, the problems are solved.

1) Let A(x,y) be the area of a rectangle not degenerated of dimensions x and y, in a way that the rectangle is inside a circle of a radius of 10. Determine the domain and the range of this function.
2) Thewave equation (c^2 ∂^2 u / ∂ x^2 = ∂^2 u / ∂ t^2) and the heat equation (c ∂^2 u / ∂

(See attached file for full problem description with proper equations)
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Two Velocities in a Traveling WaveWave motion is characterized by two velocities: the velocity with which thewave 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

(See attached for full problem description)
If electromagnetic wave equation for vacuum is where W is either magnetic B or electric E field vector, show that by using Galilean transformation wave equation will be changed to which has completely different form than given wave equation. Hence, Galilean transformation violate

An electromagnetic signal is generated by a Hertzian dipole located at a point P, which has the position vector r = ?(100m) ez. The signal is detected by a small wire loop located at the origin. Apart from the dipole and the loop, the nearby space is empty.
Experimentation reveals that the detected signal is induced by a cha

Solve the following two equations. In each case, determine dy/dx:
a.)y=xcos(2x^2)
Is this right? y'=x(-sin)(2x^2)(4x)
=-4x^2sin(2x^2)
b.)y=xe^-x^2
Is this right? y'=-xe^-x^2+1(e^-x)
=-xe^-x^2+e^-x

The question attached is from this page.
http://farside.ph.utexas.edu/teaching/em/lectures/node48.html
Please answer with vector notation. The question is only about (450) so I don't believe that you have to read through all of it to answer.

1. Two waves are traveling through the same container of nitrogen gas. Wave A has a
wavelength of 1.5 m. Wave B has a wavelength of 4.5 m. The speed of wave B must be________ the speed of wave A.
a. one-ninth
b. one-third
c. the same as
d. three times larger than
2. As thewavelength of a wave in a uniform medium inc

The vertical displacement of a string is given by y(x,t) = (6.00mm) cos[(3.25m to the power of (-1)) x - (7.22 s to the power of (-1))t]. What is thewavelength of thewave?