On a calm, cloudless afternoon the air temperature falls with height at the…

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

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

Problem

On a calm, cloudless afternoon the air temperature falls with height at the steeper-than-standard rate of

10\,\mathrm{K\,km^{-1}}

(compared with the standard lapse of

6.5\,\mathrm{K\,km^{-1}}

, for which

\mathrm{d}c/\mathrm{d}z=-0.0038\,\mathrm{s^{-1}}

and

R=90\,\mathrm{km}

, with

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

). Because the speed of sound depends on temperature in the same way in both cases,

\mathrm{d}c/\mathrm{d}z

scales linearly with the lapse rate. ((a)) Find

\mathrm{d}c/\mathrm{d}z

for the

10\,\mathrm{K\,km^{-1}}

lapse. ((b)) Find the radius of curvature

R

of a nearly horizontal ray in this air.

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