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 the wavelength of a wave in a uniform medium increases, its frequency will _____.
a. decrease
b. increase
c. remain the same

3. The speed of a wave depends upon (i.e., is causally effected by) ...
a) the properties of the medium through which the wave travels
b) the wavelength of the wave.
c) the frequency of the wave.
d) both the wavelength and the frequency of the wave.

Solution Preview

1. The answer is C. The medium is the same for both of these waves ("the same container
of nitrogen gas"). Thus, the speed of the wave will be the same. Alterations in a
property of a wave (such as wavelength) will not ...

Solution Summary

Calculation of the speed of a wave through nitrogen gas. Relationship between wave speed, wave properties, and medium properties.

See attached file for full problem description.
By explict differentiation, check that the functions f1, f2 below satisfy the waveequation.
Shwo that f4 does not.
f1(z, t) = Ae^(-b(z-vt)^2)
f2(z, t) = Asin[b(z -vt)]
f4(z, t) = Ae^(-b(bz^2 + vt))

See attached file for full problem description.
9.2 Show that the standing wave f(z,t) = Asin(kz)cos(kvt) satisfies the waveequation, and express it as the sum of a wave travelling to the left and a wave traveling to the right as shown in the following equation:
F(z,t) = g(z -vt) + h(z + vt)

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

A wave causes a displacement y that is given in meters according to y=(0.45) sin (8.0 * 3.14t - 3.14x), where t and x are expressed in seconds and meters.
a.) What is the amplitude of the wave?
b.) what is the frequency of the wave?
c.) What is the wavelength of the wave?
d.) What is the speed of the wave?
e.) Is th

The diagrams attached represent the polarization states of light. In each case the wave is traveling along the x-axis in the positive x direction.
i) Which diagram represents linear polarized light at 45 degrees?
ii) Which diagram represents left circular light? Explain.
iii) Which diagram represents un-polarized light?

Consider the wave equation for a semi-infinite string(in the domain x>or =0)
with wave speed c=1, for initial conditions u(x,0)=0 and
(u) subscript (t)(x,0)= (4x)/(1+x^2), x>or =0
Using d'alembert's solution show that the solution of the wave equation for t>or=0
is u(x,t)=In((1+(x+t)^2)/(1+(x-t)^2))
I have to consider t

Uxx means second derivative with respect to x
Uyy means second derivative with respect to y
Uxx + Uyy = 0, 0 < x < pi, 0 < y < 1
Ux(0,y) = 0 = U(pi,y), 0 < y < 1
U(x,0) = 1, U(x,1) = 0, 0 < x < pi
Please show all work including how eigenvalues and eigenvectors are derived.
Thank you

Please see the attached file for the fully formatted problems.
Consider the inhomogeneous Helmholz equation in spherical coordinates....
...
FIND that solution to this equation which
(i) is spherically symmetric, i.e. independent of theta and phi.
(ii) is finite at ...
(iii) expresses an outgoing wave i.e. ... at large (

As shown in ATTACHMENT #1, a wave is traveling toward +x on a wire. The motion of a point at x1= .45 m is shown. From the diagram, initial value of y is .12 meters and is increasing so initial slope is positive. The amplitude is .20 m, and the period is .5 sec.
From this information, develop the equation y(x,t) of the wave,