Assignment 3, Phys 2218, Fall 2013
Due MONDAY Sept. 23 in the boxes across from 121 Clark.
Concepts: Wave equation, standing waves, boundary conditions.
Problem 1 Pain 5.13
Problem 2 Pain 6.7
Problem 3 A uniform string of length 2.5m and mass 0.01 kg has
Jordan Elwood
Monday, November 4th, 2013
Force Due to Gravity
Purpose:
and
The purpose of this certain lab is to determine the relationship between gravity
the mass of an object, in relation to Earths gravitational field strength.
Hypothesis: The force do
1
I. HW 11 SOLUTIONS
Problem 1: Recall the formula we derived for the power in a running wave, P = Cvk 2 |A|2 , where C is a medium-specific constant (e.g. string tension, bulk modulus), v is the wave speed, k is the wave-vector, and A is the complex wave
1
I. HW 10 SOLUTIONS
Problem 1: The existence of evanescent waves came up in the discussion of diffraction through a slit. Although our form of the wave amplitude seemed plausible, we never actually checked that it satisfied the wave equation for a physic
1
I. HW 9 SOLUTIONS
Problem 1: A plane wave with wave-vector kx = 0, ky = k is normally incident on a screen in which there is a slit of width w. In lecture we found that the waves transmitted through the slit have a continuous distribution of kx and ^ we
1
I. HW 8 SOLUTIONS
Problem 1: The human ear can detect sound frequencies up to about 20 kHz. But sound waves exist also at higher frequencies and bats, in particular, use sound up to 120 kHz for echolocation. Is there a physical upper limit to the possib
1
I. HW 7 SOLUTIONS
Problem 1: Repeat the derivation in lecture, of the L-dependence of the kinetic energy of a gas, but for a gas of particles moving in a three dimensional cylinder of length L. There are just a few things that will change: the cross sec
1
I. HW 6 SOLUTIONS
Problem 1: Repeat the wave-packet calculation in lecture but for a different distribution of wave-vectors, h(k). Instead of a Gaussian h(k), use a narrow, flat distribution. To be precise, your h(k) should be non-zero only in the range
1
I. HW 5 SOLUTIONS
Problem 1: Express the running wave s(x, t) = H cos(kx - t), describing the vertical displacement of the surface of a fluid, in terms of two standing waves of the kind we examined in detail in lecture (hint: use the trig. rule for diff
1
I. HW 4 SOLUTIONS
Problem 1: Your part in calculating the oscillation frequencies of waves at the surface of a fluid (water waves) is to calculate the stored potential energy due to both gravity and surface tension. Start by making no assumptions about
1
I. HW 3 SOLUTIONS
2
Problem 1: At time t = 0 the current distribution on a co-axial cable has the form i(x, o) = Ae-(x/w) . The time rate of change of the current at t = 0 is zero everywhere along the cable. This is sufficient information to determine t
1
I. HW 2 SOLUTIONS
Problem 2: the most general solution of the slinky wave equation on an infinite slinky is given by s(x, t) = f (x - vt) + g(x + vt). where f and g are arbitrary functions of one variable and v is the slinky wave velocity. When challeng
1
I. HW 1 SOLUTIONS
Problem 1: A slinky with total mass M and linear force constant K hangs from the ceiling. By first representing the slinky as a chain of N equal mass points connected by equal springs, obtain a formula for the equilibrium height z(n) o
Physics 2218
Final Solutions
1
1. (15 points) A near-ideal gas (in three dimensions) of N spin-1/2 atoms fills a volume V in which there is a magnetic field B. The energy of the system, E = Ep + Es , is the sum of kinetic energy Ep = and magnetic dipole e
1
n1 n
3
A
1
n1 n2
B
Example: Prism
Screen
3,A
n3 n1 n2 n3 . The angle1 is the same in both cases A and B. For case B, how does the angle3,B that the ray makes with a normal to the interfaces when it's in the medium with refractive index n3 compare with
1
FIG. 1: Geometry for problem 1
I.
HW 12 SOLUTIONS
Problem 1: This concerns the problem analyzed in lecture, where a particle moves in a 2D potential that has two values: a higher value within circular regions of radius R and a lower value elsewhere. You
1
I. HW 13 SOLUTIONS
Problem 1: Derive the formula for the entropy of an ideal gas of N diatomic molecules, S(V,E). As for the monoatomic gas, V is the volume and E is the total energy of the gas which now includes rotational kinetic energy. In addition t
Discussion section 8
October 29, 2013
1. Barometric equation.
(a) Consider a horizontal slab of air whose thickness (height) is dz . If this slab is at rest, the pressure holding
it up from below must balance both the pressure from above and the weight of
Heat equation
1. Heat equation. Consider a uniform rod of material with density , specic
heat capacity at constant pressure cp and whose temperature varies only
along its length, in the x direction.
(a) By considering the heat owing from both left and rig
Assignment 2, Phys 2218, Fall 2013
Due Friday Sept. 13 in the boxes across from 121 Clark.
Concepts: Forced oscillators and resonance. Coupled oscillators.
Problem 1 Pain 3.11
Problem 2 Pain 3.17
Problem 3 Pain 4.5
Problem 4 Pain 4.19
Problem 5 Two harmon
Assignment 1, Phys 2218, Fall 2013
Due Friday Sept. 6 in the boxes across from 121 Clark.
Concepts: Various examples of simple harmonic motion. Damped oscillators, Forced oscillators and resonance.
Problem 1:
Pain 1.1(a) -(e), 1.1(g). For the latter you n
Discussion section 6
1
Doppler E ect
The Doppler e ect says that when the source of a wave and/or its observe are
moving towards each other, the observed frequency of a wave is greater than the
produced frequency. Similarly, if the two are moving away fro
Discussion section 7
October 22, 2013
Thin lm interference
The electric eld of the reected wave can be shown to be:
Er =
n1 n2
Ei
n1 + n 2
where Ei is the electric eld of the incident wave. If the medium that the light
goes INTO has a larger index of refr
Discussion 5
October 6, 2013
Phase and Group velocities
Say we have two travelling waves, for simplicity, with same amplitudes but
traveling with dierent speeds in the same medium:
y1
= A sin(k1 x 1 t)
y2
= A sin(k2 x 2 t)
1. Write down the total displace
Discussion 5
October 1, 2013
Phase and Group velocities
Say we have two travelling waves, for simplicity, with same amplitudes but
traveling with dierent speeds in the same medium:
y1
= A sin(k1 x 1 t)
y2
= A sin(k2 x 2 t)
1. Write down the total displace
Discussion 1
PHYS 2218
and we will determine the potential energy of the lake
by integrating this over the lake, but we also need the
height as function of x, which well take as
y (x) = 2
U=
=
dU
y0
1
gb 2
2
L
= 2gb
=
Lake oscillations
y0
x
L
2
y0 2
L2 3
1
I. PRELIM 1 SOLUTIONS
Problem 1: B,C,A Problem 2: (a) We are given that vph = c c = = k n(k) A + Bk 2 ck (k) = A + Bk 2 (1) (2)
The group velocity is given by: vgroup = d dn = c/n - ck/n2 dk dk = c/n(1 - (k/n)2Bk) = c/n2 (A - Bk 2 ) (3) (4) (5)
(b) from
1
I. HW 14 SOLUTIONS
Problem 1: In lecture we considered a system whose only degrees of freedom are the spin magnetic moments of N particles. Each spin may be in one of two directions, "up" and "down", and the energy is just the sum of the magnetic moment