Cornell University

Department of Physics

Phys 214 September 17, 2003

Waves, Optics, and Particles, Fall 2003

Homework Assignment # 4

(Due Thursday, September 25 at 5:00pm sharp.)

Agenda and readings for the week of September 22:

Skills to be mastered:

• distinguishing between speed of wave propagation and particle speed;

• understanding that the longitudinal component of tension $\tau_x$ is constant;

• getting $\tau_y$ knowing $\frac{\partial y}{\partial x}$;

• understanding that the "chunk" mass is $\mu\Delta x$;

• converting expressions like $\frac{\frac{\partial y}{\partial x}(x+\Delta x,t)-\frac{\partial y}{\partial x}(x,t)}{\Delta x}$ to the proper partial derivatives, $\frac{\partial}{\partial x}\left( \frac{\partial y}{\partial x} (x,t)\right)$, in the limit $\Delta x \rightarrow 0$;

• interpretting "snapshots" $y(x, t=t_0)$ and "particle histories" $y(x=x_0, t)$;

• understanding the boundary conditions for both fixed and free ends of a string;

• sketching allowed modes for different types of boundary conditions;

• reading the wavelength off of pictures of different standing wave modes;

• extracting allowed frequencies from allowed wavelengths;

• confirming a given $y(x,t)$ as a solution to the wave equation;

• deriving the dispersion relation $\omega = f(k)$ from the standing wave form $y(x,t) = A \cos(\omega t)\cos(kx)$;

• relating the wave speed ($v$) to the physical parameters of the system in which the waves are propagating: i.e., $v=c \equiv \sqrt{\tau/\mu}$ for a string; $v=c\equiv\sqrt{B/\rho}$ for sound.

Lectures and Readings:

Readings marked YF are from the text Young and Freedman, University Physics, 10th edition. Readings marked LN are from the course lecture notes to be found at http://www.muchomas.lassp.cornell.edu/P214.

• Lec 8, 09/23 (Tue): Maxwell's equations in vacuum; Polarization Rule I for electromagnetic waves; differential forms for Maxwell's equations.
  Readings: LN ``Other waves'' Sec. 3-3.2.4; YF 33-1, 33-2, 33-3.

• Lec 9, 09/25 (Thu): ``Let there be light''; Polarization Rule II for light.
  Readings: LN ``Other waves'' Sec. 3.2.5-4; YF 33-4.

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