Physicians use high-frequency (f = 1 MHz to 5 MHz) sound waves, called ultrasoun

Question

Physicians use high-frequency (f = 1 MHz to 5 MHz) 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 ration 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 of the heart wall? (Assume that the speed of sound in the lungs is 344 m/s.)

(b) What is the critical angle for the sound waves in air incident on muscle?

Explanation / Answer

The speed of the ultrasound waves in muscle is v1=1480 m/s the speed of the ultrasound waves in air is v2= 344 m/s According to Snell's law sin1/sin2 =v1/v2 .....................(1) where '1' is angle of incident   and '2' is the angle of refraction _____________________________________________________________________________ (a) the angle of refraction is r =9.730 from equation (1) sin 1=v1 (sin2)/v2           =1480 (sin9.73)/344 the angle of incident is 1=sin^-1(0.727116555)                                          =46.640 from equation (1) sin 1=v1 (sin2)/v2           =1480 (sin9.73)/344 the angle of incident is 1=sin^-1(0.727116555)                                          =46.640 ______________________________________________________________________________ (b) the critical angle for the sound waves in air incident on muscle is c =sin^-1(v2/v1)      =sin ^-1 (340/1480)      =13.440

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