A factory siren above flat ground radiates at each of two tones

PHYSICS · Multi-part · Fermi University Physics · Oscillations, Waves & Acoustics · Fluids & Continuum Physics · Waves, acoustics and compressible flow

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

Problem

A factory siren

4.0\,\mathrm{m}

above flat ground radiates

5.0\,\mathrm{W}

at each of two tones,

1\,\mathrm{kHz}

and

4\,\mathrm{kHz}

. The air is at

20^\circ\mathrm{C}

and

50

per cent relative humidity, uniform in temperature (

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

), with a wind whose speed rises with height at

\mathrm{d}U/\mathrm{d}z=0.10\,\mathrm{s^{-1}}

near the ground. Two villages lie

600\,\mathrm{m}

from the siren, one directly upwind and one directly downwind, with listeners

1.5\,\mathrm{m}

above the ground. Use the absorption quoted in the chapter from ISO 9613-1,

4.7\,\mathrm{dB\,km^{-1}}

1\,\mathrm{kHz}

and

30\,\mathrm{dB\,km^{-1}}

4\,\mathrm{kHz}

. ((a)) Where does the upwind shadow begin, and what does the ray picture say the upwind listener hears? ((b)) For the downwind listener, estimate the intensity level of each tone, treating the spreading as spherical and ignoring the ground. Is this estimate likely to be high or low, and why? ((c)) Beyond what distance does absorption take more decibels from each tone per doubling of distance than spherical spreading does?

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