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morpeh [17]
4 years ago
7

The Doppler effect using ultrasonic waves of frequency 2.25 × 106 Hz is used to monitor the heartbeat of a fetus. A (maximum) be

at frequency of 240 Hz is observed. Assuming that the speed of sound in tissue is 1540 m/s, calculate the maximum velocity of the surface of the beating heart.
Physics
1 answer:
miss Akunina [59]4 years ago
4 0

Answer:

v = 2.88 \times 10^7 m/s

Explanation:

As per Doppler's effect we know that the frequency of the sound that is observed by the detector is the reflected sound

This reflected sound is given as

f' = f (\frac{v - v_h}{v + v_h})

f' = 2.25\times 10^6(\frac{v - 1540}{v + 1540})

so we know that the beat frequency is

\Delta f = 240 Hz

so we will have

f - f' = \Delta f

2.25 \times 10^6 - 2.25\times 10^6(\frac{v - 1540}{v + 1540}) = 240

1 - (\frac{v - 1540}{v + 1540}) = 1.07 \times 10^{-4}

so we have

0.99989 = (\frac{v - 1540}{v + 1540})

1.99989\times 1540 = 1.067 \times 10^{-4} v

v = 2.88 \times 10^7 m/s

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