\[f' = f\left(\frac{c+v_o}{c-v_s}\right)\]
Variables
fpobserved frequency (Hz)
fsource frequency (Hz)
cspeed of sound (m/s)
voobserver velocity relative to medium (m/s)
vssource velocity relative to medium (m/s)
Description
What is this formula?
The Doppler Shift for Sound calculates the frequency perceived by an observer when there is relative motion between the sound source and the observer. Motion toward each other increases the observed frequency, while motion away decreases it.
When to use it
Use this formula when analyzing moving sound sources, vehicle sirens, radar calibration experiments, acoustical measurements, and wave propagation problems involving relative motion.
Example
Given:
f = 500 Hz
c = 343 m/s
vo = 0 m/s
vs = 20 m/s
Formula:
f' = f((c + vo)/(c - vs))
Substitution:
f' = 500((343 + 0)/(343 - 20))
f' = 500(343/323)
f' = 531 Hz
Result:
f' ≈ 531 Hz
Applications
Vehicle sirens.
Acoustic measurements.
Wave motion studies.
Medical ultrasound Doppler systems.
Astronomy and remote sensing analogies.