The Hummingbird's Wing Harmonics · AI Generator #GEN-7BA3B4C0

Physics

Problem

A ruby-throated hummingbird hovers by beating its wings at a frequency of

f_0 = 53\;\text{Hz}

. Each wing stroke creates a sound pulse that travels through air at

v = 343\;\text{m/s}

. An observer initially at rest begins walking directly toward the hovering hummingbird at a constant speed of

v_w = 1.2\;\text{m/s}

. Due to the Doppler effect, the observer hears a shifted frequency. However, because the hummingbird's wings beat on both the upstroke and downstroke, the observer actually hears two overlapping Doppler-shifted frequencies corresponding to sound pulses emitted when the wing tips are moving toward and away from the observer. Assuming the wing tips move at

v_{tip} = 8.5\;\text{m/s}

toward and away from the observer during different parts of the wing stroke, calculate the beat frequency that the walking observer hears due to the superposition of these two Doppler-shifted sound waves.

Browse the problem library