a red blood cell travels at a speed of 40 cm/s in a large artery. a sound with a frequency of 100 kHz enters a blood opposite the direction flow. calculate the frequency of sound reflected from the cell and detected by a receiver. (v = 1500 m/s)
deltaf/f = 2*v'/v
deltaf is the shift in frequency
v' is the cell velocity = 0.4 m/s
v is the sound velocity in blood = 1500 m/s
f = 100 kHz.
deltaf = 2(0.4/1500)*100 kHz = 0.053 kHz
The received frequency is 1500.053 kHz
(1500+0.4)/(1500-0.4)]*(100000)
To calculate the frequency of sound reflected from the red blood cell and detected by a receiver, we can use the Doppler effect equation:
f' = (v + vr) / (v + vs) * f
where:
f' is the received frequency
v is the speed of sound in the medium (given as 1500 m/s)
vr is the velocity of the receiver (assumed to be zero in this case since it is not given)
vs is the velocity of the source (red blood cell in this case)
f is the frequency of the sound wave (100 kHz or 100,000 Hz)
To apply this equation, we need to convert the speed of the red blood cell from cm/s to m/s:
vs = 40 cm/s * (1 m/100 cm) = 0.4 m/s
Now let's substitute the given values into the equation and solve for f':
f' = (1500 m/s + 0.4 m/s) / (1500 m/s + 0.4 m/s) * 100,000 Hz
f' = (1500.4 m/s) / (1500.4 m/s) * 100,000 Hz
f' = 100,000 Hz
Therefore, the frequency of sound reflected from the red blood cell and detected by the receiver is still 100,000 Hz.
To calculate the frequency of sound reflected from the red blood cell and detected by the receiver, we can use the principle of the Doppler effect.
The Doppler effect describes the change in frequency of a wave (in this case, sound) due to the relative motion between the source and the observer. It is given by the equation:
f' = (v + vr) / (v + vs) * f
Where:
- f' is the observed frequency (frequency detected by the receiver)
- v is the speed of sound in the medium (given as 1500 m/s)
- vr is the velocity of the red blood cell (opposite to the direction of sound flow)
- vs is the velocity of the sound source (blood flow)
Given:
- Sound frequency, f = 100 kHz = 100,000 Hz
- Red blood cell velocity, vr = -40 cm/s = -0.4 m/s
To calculate vs, the velocity of the sound source in the blood, we need to consider the relative velocity between the blood flow and the cell. Since the cell travels opposite to the direction of blood flow, we can add their velocities:
vs = 0 - (-40 cm/s) = 40 cm/s = 0.4 m/s
Now, we can substitute the given values into the Doppler effect equation:
f' = (v + vr) / (v + vs) * f
= (1500 m/s - 0.4 m/s) / (1500 m/s + 0.4 m/s) * 100,000 Hz
Calculating this expression will give us the frequency of sound reflected from the red blood cell and detected by the receiver.