• Energy flux, $S$:
  • The amount of energy passing through a unit surface area per unit time.
• Intensity, $I$:
  • The average energy flux, i.e. $I = \langle S \rangle$.

• SI unit for $S$ and $I$: $W/m^2$.
• $1W = 1J/s$.
• For example, $I= 1000W/m^2$ means an area of $1m^2$ will receive $1000J$ of energy every second. This is about the intensity of direct sunlight around noon.

If the power at the source is $P$ (power is measured in $W$), then at distance $r$ the power has to be spread out over a spherical area of $4\pi r^2$, producing the intensity:

The decibel scale

The human perception of "loudness" turns out is not proportional the intensity $I$. Instead, it corresponds to the sound pressure level (SPL) $\beta$ (sometimes also know as the sound intensity level): where $I_0 = 10^{-12}W/m^2$, and $dB$ is unit the decibel. The $\log$ is taken with base $10$.

Reminder about $\log$:

• $\log 10^n = n$.
• $\log (ab) = \log a + \log b$.

Sound	$\beta$ ($dB$)	$I$ ($W/m^2$)
Threshold of hearing	$0$	$10^{-12}$
Whisper	$20$	$10^{-10}$
Conversation	$60$	$10^{-6}$
Painfully loud	$120$	$1$

The Doppler effect (or the Doppler shift) is the change in frequency of a wave in relation to an observer who is moving relative to the wave source.

Suppose a source $S$ produces a sound at frequency $f_S$. The frequency $f_L$ as observed by the listener is given by:

where $c = 340m/s$ is the speed of sound, $v_S$ and $v_L$ are the velocities of the source and the listener relative to the air.

The signs of $v_S$ and $v_L$ are defined by the "$L$ to $S$" arrow, as explained in the figure below. For example, if the source is traveling at $5m/s$ in the opposite direction to the "$L$ to $S$" arrow, then you must put $v_S = -5m/s$ in the equation for Doppler effect above.