The Doppler effect using ultrasonic waves of frequency 2.23×106 Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 258 Hz is observed. Part A Assuming that the speed of sound in tissue is 1.54×103m/s, calculate the maximum velocity of the surface of the beating heart.

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wagonbelleville wagonbelleville · Answer 1 · 2019-12-06T08:49:20+01:00

Answer:

v = 8.89 cm/s

Explanation:

given,

frequency of ultrasonic wave = 2.23 x 10⁶ Hz

beat frequency = 258 Hz

speed of sound in the tissue = 1.54×10³ m/s

maximum velocity = ?

using Doppler equation

[tex]f_1 = f_0 (\dfrac{c+ v}{c})[/tex]..........(1)

[tex]f_2 = f_1 (\dfrac{c}{c-v})[/tex]..........(2)

now, from equation (1) and (2)

[tex]f_2 = f_0 (\dfrac{c + v}{c-v})[/tex]

f₂ = 2.23 x 10⁶ + 258 = 2230258 Hz

f₀ = 2.23 x 10⁶ Hz

c = 1540 m/s

[tex]2230258= 2230000(\dfrac{1540+ v}{1540-v})[/tex]

1.00012(1540 - v ) = 1540+ v

1540.178 - 1.00012 v = 1540 + v

2.00012 v = 0.178

v = 0.08899 m/s

v = 8.89 cm/s