A fixed siren on a hilltop emits a pure tone at in still air,

PHYSICS · Subjective · Fermi University Physics · Oscillations, Waves & Acoustics · Fluids & Continuum Physics · Wave motion, the wave equation and wave energy

Signal Speeds in Fluids, Ch Sound in a moving, absorbing fluid: sources, refraction and loss

Problem

A fixed siren on a hilltop emits a pure tone at

f_0=500\,\mathrm{Hz}

in still air,

c_0=343.2\,\mathrm{m\,s^{-1}}

. A steady wind of

U=15\,\mathrm{m\,s^{-1}}

blows directly from the siren towards a stationary listener

1\,\mathrm{km}

away. Someone argues: "the wind carries the sound faster towards the listener, at effective speed

c_0+U

instead of

c_0

. By the same reasoning as the Doppler effect, the listener should hear a raised frequency

f = f_0\frac{c_0+U}{c_0} = 500\times\frac{343.2+15}{343.2} = 521.8\,\mathrm{Hz}.

" Find the error in this argument, and state what frequency the listener actually hears and what does change because of the wind.

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