# Homework #3, 2013

*Due on Day 8 (Wednesday) at 5pm*

## Q1: Physics Journals

**a)** Read the journal club assignment.
Find a third appropriate article in one of the listed journals (you should have found your first two articles as part of HW1 and HW2).
Read the article. Write down the first author, article title, journal name, journal volume, page number and year of the article. Write a one paragraph summary of the article.

**b)** Together with your partner, identify the best article for your presentation (out of the 6 or more articles that you have collectively read).

## Q2: Forbidden Frequencies

Consider the system of coupled pendulums you studied in Homework #2. Use a sketch to qualitatively describe the motion of masses that results from driving one mass at an angular frequency that is lower than sqrt(*g* / *L*) (all other masses are initially at equilibrium).

Hints: Will neighboring masses move? Will distant masses move? Will any normal modes be excited? Can the situation be described using the concept of a penetration depth?

Note for next year: It is easier to draw a semi-infinite chain of coupled pendulum (it has a beginning, but no end) and then consider driving the mass at the end.

## Q3: 1-d diatomic lattice

Consider a 1-dimensional diatomic lattice. The atomic spacing is 0.3 nm, the maximum frequency of the acoustic branch is 10^13 rad/s, and the long-wavelength frequency of the optic branch is 1.594 x 10^13 rad/s.

**a)** Calculate the speed of sound in this 1-dimensional crystal. First explain which region of the dispersion relation you will use to calculate this and why. Then find an expression for the velocity that makes use of the parameters given in the problem.