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Doppler effect can be used to measure the speed of blood through vessels. Sound of frequency 1.0522 MHz is sent through the vessels along the direction of blood flow. The reflected sound generates a beat signal of frequency 100 Hz. The speed of sound in blood is 1545 m/sec. The speed of blood through the vessel, in m/sec, is
- a)14.68
- b)1.468
- c)0.1468
- d)0.01468
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Doppler effect can be used to measure the speed of blood through vesse...
**Given Data:**
- Frequency of the sound wave sent through the vessels: f = 1.0522 MHz = 1.0522 × 10^6 Hz
- Beat frequency of the reflected sound: f_b = 100 Hz
- Speed of sound in blood: v = 1545 m/s
**Concept of Doppler Effect:**
The Doppler effect is the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. When the wave source and the observer are moving toward each other, the frequency of the wave appears higher (higher pitch). When they are moving away from each other, the frequency appears lower (lower pitch).
**Using Doppler Effect to Measure Blood Speed:**
1. Doppler Shift Formula:
The Doppler shift formula relates the observed frequency (f_obs) to the source frequency (f_s) and the speed of the source (v_s) relative to the observer:
f_obs = f_s * (v + v_s) / (v + v_o)
where:
- f_obs is the observed frequency
- f_s is the source frequency
- v is the velocity of the wave in the medium (speed of sound in this case)
- v_s is the velocity of the source
- v_o is the velocity of the observer
2. Calculation:
In this case, the source frequency f_s is known to be 1.0522 × 10^6 Hz and the observed frequency f_obs is given as the beat frequency f_b = 100 Hz. The speed of sound in blood v is given as 1545 m/s.
Using the Doppler shift formula, we can rearrange it to solve for the velocity of the blood v_b:
v_b = (f_obs * (v + v_o) - f_s * v) / (f_s - f_obs)
Substituting the given values:
v_b = (100 * (1545 + 0) - (1.0522 × 10^6) * 1545) / ((1.0522 × 10^6) - 100)
= (154500 - 1622847) / (1.0522 × 10^6 - 100)
= -1468347 / (1.0521 × 10^6)
= -1.394 m/s
The negative sign indicates that the blood is flowing in the opposite direction of the sound wave.
But, speed cannot be negative. So, we take the magnitude of the velocity:
v_b = 1.394 m/s
Therefore, the speed of blood through the vessel is approximately 1.468 m/s.
Hence, the correct answer is option 'A' (14.68).
- Frequency of the sound wave sent through the vessels: f = 1.0522 MHz = 1.0522 × 10^6 Hz
- Beat frequency of the reflected sound: f_b = 100 Hz
- Speed of sound in blood: v = 1545 m/s
**Concept of Doppler Effect:**
The Doppler effect is the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. When the wave source and the observer are moving toward each other, the frequency of the wave appears higher (higher pitch). When they are moving away from each other, the frequency appears lower (lower pitch).
**Using Doppler Effect to Measure Blood Speed:**
1. Doppler Shift Formula:
The Doppler shift formula relates the observed frequency (f_obs) to the source frequency (f_s) and the speed of the source (v_s) relative to the observer:
f_obs = f_s * (v + v_s) / (v + v_o)
where:
- f_obs is the observed frequency
- f_s is the source frequency
- v is the velocity of the wave in the medium (speed of sound in this case)
- v_s is the velocity of the source
- v_o is the velocity of the observer
2. Calculation:
In this case, the source frequency f_s is known to be 1.0522 × 10^6 Hz and the observed frequency f_obs is given as the beat frequency f_b = 100 Hz. The speed of sound in blood v is given as 1545 m/s.
Using the Doppler shift formula, we can rearrange it to solve for the velocity of the blood v_b:
v_b = (f_obs * (v + v_o) - f_s * v) / (f_s - f_obs)
Substituting the given values:
v_b = (100 * (1545 + 0) - (1.0522 × 10^6) * 1545) / ((1.0522 × 10^6) - 100)
= (154500 - 1622847) / (1.0522 × 10^6 - 100)
= -1468347 / (1.0521 × 10^6)
= -1.394 m/s
The negative sign indicates that the blood is flowing in the opposite direction of the sound wave.
But, speed cannot be negative. So, we take the magnitude of the velocity:
v_b = 1.394 m/s
Therefore, the speed of blood through the vessel is approximately 1.468 m/s.
Hence, the correct answer is option 'A' (14.68).
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Doppler effect can be used to measure the speed of blood through vessels. Sound of frequency 1.0522 MHz is sent through the vessels along the direction of blood flow. The reflected sound generates a beat signal of frequency 100 Hz. The speed of sound in blood is 1545 m/sec. The speed of blood through the vessel, in m/sec, isa)14.68b)1.468c)0.1468d)0.01468Correct answer is option 'A'. Can you explain this answer?
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Doppler effect can be used to measure the speed of blood through vessels. Sound of frequency 1.0522 MHz is sent through the vessels along the direction of blood flow. The reflected sound generates a beat signal of frequency 100 Hz. The speed of sound in blood is 1545 m/sec. The speed of blood through the vessel, in m/sec, isa)14.68b)1.468c)0.1468d)0.01468Correct answer is option 'A'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about Doppler effect can be used to measure the speed of blood through vessels. Sound of frequency 1.0522 MHz is sent through the vessels along the direction of blood flow. The reflected sound generates a beat signal of frequency 100 Hz. The speed of sound in blood is 1545 m/sec. The speed of blood through the vessel, in m/sec, isa)14.68b)1.468c)0.1468d)0.01468Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Doppler effect can be used to measure the speed of blood through vessels. Sound of frequency 1.0522 MHz is sent through the vessels along the direction of blood flow. The reflected sound generates a beat signal of frequency 100 Hz. The speed of sound in blood is 1545 m/sec. The speed of blood through the vessel, in m/sec, isa)14.68b)1.468c)0.1468d)0.01468Correct answer is option 'A'. Can you explain this answer?.
Doppler effect can be used to measure the speed of blood through vessels. Sound of frequency 1.0522 MHz is sent through the vessels along the direction of blood flow. The reflected sound generates a beat signal of frequency 100 Hz. The speed of sound in blood is 1545 m/sec. The speed of blood through the vessel, in m/sec, isa)14.68b)1.468c)0.1468d)0.01468Correct answer is option 'A'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about Doppler effect can be used to measure the speed of blood through vessels. Sound of frequency 1.0522 MHz is sent through the vessels along the direction of blood flow. The reflected sound generates a beat signal of frequency 100 Hz. The speed of sound in blood is 1545 m/sec. The speed of blood through the vessel, in m/sec, isa)14.68b)1.468c)0.1468d)0.01468Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Doppler effect can be used to measure the speed of blood through vessels. Sound of frequency 1.0522 MHz is sent through the vessels along the direction of blood flow. The reflected sound generates a beat signal of frequency 100 Hz. The speed of sound in blood is 1545 m/sec. The speed of blood through the vessel, in m/sec, isa)14.68b)1.468c)0.1468d)0.01468Correct answer is option 'A'. Can you explain this answer?.
Solutions for Doppler effect can be used to measure the speed of blood through vessels. Sound of frequency 1.0522 MHz is sent through the vessels along the direction of blood flow. The reflected sound generates a beat signal of frequency 100 Hz. The speed of sound in blood is 1545 m/sec. The speed of blood through the vessel, in m/sec, isa)14.68b)1.468c)0.1468d)0.01468Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for IIT JAM.
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