Doppler Effect (Approaching Observer)

When you move toward a stationary source, the waves themselves are unchanged — you simply run into them more often. Cycling at 10 m/s toward a 500 Hz factory whistle in 343 m/s air, you intercept 500 × (343 + 10)/343 ≈ 515 Hz, a shift of 15 Hz. Unlike the moving-source case there is no runaway denominator: even sprinting at the speed of sound toward the whistle would only double the frequency, because the waves keep their spacing and you just sweep through them faster.

That asymmetry — moving source squeezes the wavelength, moving observer changes only the encounter rate — is a favorite exam trap, and the two formulas give slightly different answers for the same relative speed. At everyday speeds the difference is tiny: both predict about a 3% shift at 10 m/s. Bats live by this physics, correcting their echolocation chirps for their own flight speed so the returning echo lands in the narrow frequency band where their ears are sharpest.