The beat frequency produced by an ultrasound reflected from a bloodstream moving at 27.0 cm/s, given an original frequency of 3.50 MHz, is calculated using the Doppler effect formula and is approximately 613.64 Hz.
To determine the beat frequency produced by an ultrasound reflected from a moving bloodstream, we can use the Doppler effect formula. The original frequency is given as 3.50 MHz (which is equivalent to 3,500,000 Hz), and the bloodstream is moving towards the source at a speed of 27.0 cm/s.
The Doppler effect equation for frequency received (f') when a source and observer are moving closer together is:
f' = f(1 + v/vs)
Where:
f' is the observed frequency
f is the source frequency (3,500,000 Hz)
v is the velocity of the blood (27.0 cm/s)
vs is the velocity of sound in tissue (1540 m/s)
First, convert the speed of the blood to meters per second:
v = 27.0 cm/s = 0.27 m/s
Now, plug the values into the equation:
f' = 3,500,000 Hz (1 + 0.27 m/s / 1540 m/s)
Calculate the observed frequency:
f' ≈ 3,500,000 Hz (1 + 0.0001753246753)
f' ≈ 3,500,000 Hz + 613.63636364 Hz
f' ≈ 3,500,613.63636364 Hz
The beat frequency is the absolute difference between the observed frequency and the source frequency:
Beat frequency = |f - f'|
Beat frequency = |3,500,000 Hz - 3,500,613.64 Hz|
Beat frequency ≈ 613.64 Hz
Therefore, the beat frequency is approximately 613.64 Hz.