Question

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

Answer 1

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

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

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

$v = 2.88 \times 10^7 m/s$