Question

A sound wave is traveling in warm air when it hits a layer of cold, dense air. If the sound wave hits the cold air interface at an angle of 20 ?, what is the angle of refraction? Assume that the cold air temperature is -10 ?C and the warm air temperature is +20 ?C. The speed of sound as a function of temperature can be approximated by v=(331+0.60T)m/s, where T is in ?C. Express your answer to two significant figures and include the appropriate units.

Answer 1

We know that

n1*sin A1 = n2*sin A2

n1, n2 = index of refraction for different mediums

A1 = angle of incidence

A2 = angle of refraction

for different mediums

n = c/v

which means refrative index is inversely proportional to the speed of sound in that medium

n1/n2 = v2/v1

Speed and temperature relation is given by:

v = 331 + 0.60*T

when T = -10 C

v2 = 331 + 0.6*(-10) = 325 m/sec

when T = 20 C

v1 = 331 + 0.6*(20) = 343 m/sec

So

Sin A2/SinA1 = n1/n2 =v2/v1

SinA2 = (v2*sin A1)/v1

Using given values:

sin A2 = (325*sin 20 deg)/343 = 0.32407

A2 = arcsin 0.32407 = 18.9 deg

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