# Study Notes: SAT Physics Subject Test

## Waves

Basic equation: $\small v=\lambda f$; $\small \lambda =vT$

Stretched String: $\small v=\sqrt{\frac{F_{T}}{\mu}}$ ($\small \mu=m/L$)

#### Standing waves

Fundamental standing wave: $\small f_{1}=\frac{v}{2L}$

Standing wave: $\small f_{n}=nf_{1}=\frac{nv}{2L}$

#### Sound waves

Intensity: $\small I=\frac{P}{A}$ (P is the power produced by the source and A is the area over which the power is spread.)

Decibel level: $\small \beta=10log(\frac{I}{I_{0}})$ ($\small I_{0}=10^{-12}W/m^{2}$)

Beat: $\small f_{\text{beat}}=|f_{1}-f_{2}|$

#### Resonance for sound waves

If the far end of tube is sealed, for any odd integer n: $\small \lambda_{n}=\frac{4L}{n}, \, f_{n}=n \frac{v}{4L}$

If the far end of tube is not sealed, for any integer n: $\small \lambda_{n}=\frac{2L}{n}, \, f_{n}=n \frac{v}{2L}$

#### The Doppler effect

The shift in frequency that occures when the source and detector are in relative motion is known as the Doppler effect.

$\small f_{D}=\frac{v \pm v_{D}}{v \mp v_{S}} \cdot f_{s}$

When a detector approaches a source or a source approaches a detector, the resulting frequency would increase and vice versa.