Respuesta :
2.49 cm/s is the maximum speed of vibrating heart.
Given,
Frequency of ultrasonic wave = 2.57 MHz = 2.57 ×[tex]10^{6}[/tex] Hz
Speed of ultrasound = 1540m/s
The maximum frequency shift = 100 Hz
Maximum speed of heart = ?
By using Doppler equation
[tex]f1 = f0(\frac{c + v}{c} )[/tex] …..(1)
[tex]f2 = f1 (\frac{c}{c - v} )[/tex] ….. (2)
From equation (1) & (2)
[tex]f2= f0(\frac{c+v}{c-v} )[/tex]
[tex]f2 = 2.57[/tex] ×[tex]10^{6} + 100 = 2570100[/tex] Hz
[tex]f0 = 2570000[/tex] Hz
c = 1540 m/s
So,
[tex]2570100 = 2570000(\frac{1540 + v}{1540 - v} )[/tex]
1.00003(1540-v) = 1540+v
1540.05 - 1.00003v = 1540 +v
2.00003v = 0.05
v= 0.0249 m/s
v= 2.49 ×[tex]10^{-2}[/tex] m/s
v= 2.49 cm/s
So, the maximum speed of vibrating heart is 2.49 cm/s
Learn more about Doppler equation here https://brainly.com/question/14082883
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