The approaching Doppler shift is given by \( f' = f \frac{v}{v - v_s} \), with the sign convention that we subtract the source’s speed when it moves toward the observer. For a train at 20 m/s, if speed of sound is 340 m/s and horn frequency is \( f \), the observed frequency increases to \( f' = f \left( \frac{340}{320} \right) \).
Every evening, I hear the Bangalore-Mysore express approaching the crossing near our flat, its horn sharpening exactly this way—a textbook example I point out to my students, though my own father, a railway clerk for thirty years, always just called it “the train’s hurry sound.
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