• Frequency $f=1/T$

• Angular frequency $\omega =2\pi f=2\pi /T$

• Spring $T=2\pi \sqrt{m/k}$

• Pendulum $T=2\pi \sqrt{L/g}$

• Wave $f=v/\text{λ}$

• Displacement is a function of x and t:

  $$D\left(x\text{,}t\right)=A\text{sin}(kx\mp \omega t+{\varphi }_0)$$

• $-\omega t$ for motion to the right

• $+\omega t$ for motion to the left

• The wave number is $k=2\pi /\text{λ}$

• String $v=\sqrt{T_{\text{s}}/\mu }$

• Sound $v=\sqrt{B/\rho }$

• The quantity $\omega t+{\varphi }_0$ is called the phase $\varphi$ of SHM.

• The quantity $kx-\omega t+{\varphi }_0$ is the phase $\varphi$ of a sinusoidal wave.

• The phase constant ${\varphi }_0$ is given by the initial conditions.

A frequency shift when the source moves relative to an observer:

for an approaching/receding source.

Two waves traveling in opposite directions.

• Strings, open-open tubes, and closed-closed tubes:

  $$\begin{array}{c}{f}_m=m{f}_1\hfill \\ f_1=v/2L=\text{fundamental frequency}\hfill \end{array}$$

• Standing waves have points that never move called nodes.

  

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• Constructive interference if in phase

  $$\text{Δ}\varphi =m\cdot 2\pi \text{rad}$$

• Destructive interference if out of phase

  $$\text{Δ}\varphi =(m+\frac{1}{2})\cdot 2\pi \text{rad}$$

• Beats $f_{\text{beat}}=|f_1-f_2|$ if frequencies differ.