Lecture 1

Waves §

Sound Waves vs. EM Waves §

1. Sound waves need a medium
2. $V_s=300\frac{m}{s}<V_{EM}=3\cdot 10^8\frac{m}{s}$
3. Sound waves are longitudinal. EM Waves are transverse.
4. Density vs Electric Field (Magnetic Fields)

Longitudinal Wave vs. Transverse Wave

Forms of Waves §

Pulse

Periodic Wave

Important Characteristics §

$$\begin{gathered} \lambda =\text{wavelength} \\ T=\text{period} \\ v=\frac{\lambda }{T} \\ f=\frac{1}{T} \\ v=\lambda f \end{gathered}$$

Fd Traveling Wave §

Stationary (left) vs. Traveling Perspective (right)

$$\begin{gathered} y=f(x\pm vt):\text{general form of traveling wave} \\ y=A\sin [k(x-vt)] \\ y=A(x+vt{)}^2 \\ y=e^{k(x-vt)} \end{gathered}$$

Wave Equation §

$$\begin{gathered} y=f(x^{\prime }) \\ {x}^{\prime }=x-vt \\ \frac{d^{2}y}{d{x}^2}=\frac{1}{v^2}\frac{d^2}{d{t}^2} \end{gathered}$$