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Doppler Effect (Sound)

πŸ“Š intermediate
$$f' = f\left(\frac{v \pm v_o}{v \mp v_s}\right)$$
Observed frequency change due to relative motion.
Variables & Units
$f'$
Observed frequency
Unit: $\text{Hz}$
$f$
Source frequency
Unit: $\text{Hz}$
$v$
Speed of sound in medium
Unit: $\text{m/s}$
$v_o$
Observer speed (relative to medium)
Unit: $\text{m/s}$
$v_s$
Source speed (relative to medium)
Unit: $\text{m/s}$
Key Information
πŸ“ Derived From
Wavefront compression/rarefaction.
πŸ’‘ Example
Ambulance siren at $f=500\,\text{Hz}$ moving toward you at $30\,\text{m/s}$ ($v=343\,\text{m/s}$): $f' = 500\left(\frac{343}{343-30}\right) \approx 548\,\text{Hz}$.
πŸ”§ Applications
Radar speed guns, ultrasound blood flow, astronomy (redshift).
⚠️ Constraints
Non-relativistic speeds, sound in stationary medium.

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