(See attached file for full problem description with proper equations)

---
Two Velocities in a Traveling Wave
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
.
Part A
Find the velocity of propagation of this wave.
Express the velocity of propagation in terms of some or all of the variables , , and .
= ______________

Part B
Find the y velocity of a point on the string as a function of and .
Express the y velocity in terms of , , , , and .
= ____________________

Part C
Which of the following statements about , the x component of the velocity of the string, is true?

has the same mathematical form as but is out of phase.

Part D
Find the slope of the string as a function of position and time .
Express your answer in terms of , , , , and .
= ___________________
---

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 inc

1) Explain in your own words:
a) How is simple harmonic oscillation defined?
b) What is de Broglie wavelength?
c) Why will one not see an interference pattern for white light in the case of two slits?
d) Explain the expression wavelength so that your 10 year old brother can understand.
e) What is the difference between the

The expected value of the momentum operator in quantum mechanics can be calculated using the spatial wave function. Using that the momentum wave function is the Fourier transform of the spatial wave function we obtain an expression for this expected value in term of the momentum wave function, that is, we prove the Equation 15.6

1. An ocean wave travels 10.8 m in 6.9 s. The distance between two consecutive wave crests is 4.3 m. What is the frequency of the wave? Answer in units of Hz
2. Water waves in a lake travel 4.73 m in 1.01 s. The period of oscillation is1s.
What is the speed of the water waves? What is their wavelength
3. If you slosh the wate

The resolving power of a microscope is proportional to the wavelength used. A resolution of approximately 1.0 x 10-11 m (0.01 nm) would be required in order to "see" an atom. (a) If electrons were used (electron microscope), what minimum kinetic energy would be required for the electrons? (b) If phtons were used, what minimum p

A plane progressive harmonic wave is represented by the equation (see attached) where is the displacement in meters, t is the time in seconds and x is distance from a fixed origin in meters.
Determine the following waveproperties, and where appropriate give units:
a) The amplitude
b) The direction of wave travel
c) Th

A uniform rope of mass m and length L hangs from a ceiling.
(a) Show that the speed of a transverse wave in the rope is a function of y, the distance from the
lower end, and is given by v = Sqrt(gy).
(b) Show that the time it takes a transverse wave to travel the length of the rope is given by t =
2sqrt(L/g). (Hint: calculat

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

See attached file for full problem description.
9.2 Show that the standing wave f(z,t) = Asin(kz)cos(kvt) satisfies the wave equation, 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)