Question

An ultrasound unit is being used to measure a patient's heartbeat by combining the emitted 2.0 MHz signal with the sound waves reflected from the moving tissue of one point on the heart. The beat frequency between the two signals has a maximum value of 560 Hz . What is the maximum speed of the heart tissue? The speed of ultrasound waves in human tissue is 1540 m/s.
Express your answer to two significant figures and include the appropriate units.

Answer 1

Hi there, 
for this question we have:
Signal 2.0 MHz = Emitted so we can call it $f_e$
and we need the Reflected = $f_{r}$
In this question, we have a source which goes to the heart and a reflected which comes back from the heart and we need the speed of the reflected.
So you should know that the speed of reflected is lower than the source(Emitted). 
we also know: ΔBeat frequency(max) = 560 Hz = $f_{b}$
so we have: 
$f_{e}$ - $f_{r}$ = $f_{b}$
so frequency of Reflected is: 
2.0 × 10^6 Hz - 560 Hz = 1.99 × 10^6 Hz = $f_{r}$
now you know that Lambda = v/f 
so if we find the lambda with our Emitted then we can find v with the Reflected: 
Lambda = 1540(m/s) / 2.0 × 10^6 Hz = 7.7 × 10^-4 m 
=> $v_{max}$ = (lambda)($f_{r}$ 
=> 7.7 × 10^-4m (1.99 × 10^6Hz) = 1532 m/s 
so the $v_{max}$ is equal to 1532 m/s :)))
This question is solved by two top teachers as fast as they could :))
I hope this is helpful
have a nice day