Question

An echocardiogram uses sound to measure blood flow and heart function. (I’ve had this done, it...

An echocardiogram uses sound to measure blood flow and heart function. (I’ve had this done, it is cool to watch!) Assume you have 2.5 MHz ultrasound waves echoing back from the walls of the beating heart. When you add together the source sound wave with the echo you get a 535 Hz beat frequency. How fast is the wall of the heart moving?

Given beat frequency f​​​​​b = 535 Hz

We know that beat freq = freq of echo(f​​​​​​e) - freq of source(f​​​​​​s).

f​​​​​​e = fs + f​​​​​​b

fe = 2.5×10^6 +535 Hz

Using Doppler shift formula,

fe ={ v/(v-v​​​​s )}fs

Where, v = velocity of ultrasound, = 1580m/s (avarage value in human body)

v​​​​​​s = velocity of source, (here we consider reflecting wall of heart as source of eco)

Putting values,

2.5×10^6 + 535 ={ 1580/1580-vs }2.5×10^6

1.000214 = 1580/1580-vs

1-vs/1580 = 0.999786046

v​​​​​​s = (1-0.999786046)1580 = 0.338 m/s

so the wall of heart is moving with speed sf 0.338 m/s.

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