Two situations bend waves by a gradient in speed.

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

Two situations bend waves by a gradient in speed. ((a)) A tsunami of period

15\,\mathrm{min}

crosses depth contours that run parallel to a straight coast. In water of depth

h_1 = 50\,\mathrm{m}

its crests make an angle

\theta_1 = 40^\circ

with the depth contours. Using the shallow-water wave speed

c=\sqrt{gh}

and Snell's law

\sin\theta/c = \text{const}

along the ray, find the angle

\theta_2

the crests make with the depth contours in water of depth

h_2 = 8\,\mathrm{m}

. ((b)) A steady wind blows over flat ground with speed increasing linearly with height at the rate

\mathrm{d}U/\mathrm{d}z = 0.15\,\mathrm{s^{-1}}

, while the sound speed

c_0 = 343\,\mathrm{m\,s^{-1}}

is uniform with height. A source and a listener each stand at height

2\,\mathrm{m}

above the ground, the listener directly upwind of the source. Find the radius of curvature

R

of a nearly horizontal ray travelling upwind, and the distance beyond which the listener lies in the acoustic shadow.

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