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.

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

..........(1)

..........(2)

now, from equation (1) and (2)

f₂ = 2.23 x 10⁶ + 258 = 2230258 Hz

f₀ = 2.23 x 10⁶ Hz

c = 1540 m/s

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