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Chapter 5: Q37P (page 1107)

Physicians use high-frequency 1f = 195 MHz2 sound waves, called ultrasound, to image internal organs. The speed of these ultrasound waves is 1480 m>s in muscle and 344 m/s in air. We define the index of refraction of a material for sound waves to be the ratio of the speed of sound in air to the speed of sound in the material. Snell’s law then applies to the refraction of sound waves. (a) At what angle from the normal does an ultrasound beam enter the heart if it leaves the lungs at an angle of 9.73° from the normal to the heart wall? (Assume that the speed of sound in the lungs is 344 m/s.) (b) What is the critical angle for sound waves in air incident on muscle?

Short Answer

Expert verified

(a) The angle at which the beam enters the heart is 47.01°

(b) The critical angle at which the beam enters the air is 13.44°

Step by step solution

01

Snell’s law

Snell’s law;

The refractive index of medium a isna

The incident angle in the medium a isθa

The refractive index of medium b isnb

The incident angle in the medium b isθb

02

The angle at which the beam enters the heart

A substance's index of refraction is defined as the ratio of the speed of sound in air to the speed of sound in the material. As a result, the muscle's refractive index will be;

nmuscle=3441480=0.2324

The speed of waves in air is 344m/s

The speed of the waves in muscles is 1480m/s

  1. Incident angle is

So, the angle is;

Hence, the angle at which the beam enters the heart is47.01°

03

The critical angle at which the beam enters the air

(b) For the critical angle in the air, the wave should leave at an angle of 90°

Thus, using Snell’s law;

Hence, the critical angle at which the beam enters the air is13.44°

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