Concept explainers
(a)
The maximum linear speed of the heart wall.
(a)
Answer to Problem 40P
The maximum linear speed of the heart wall is
Explanation of Solution
Write the expression for the maximum speed.
Here,
Write the expression for the angular velocity.
Here,
Conclusion:
Substitute
Substitute
Therefore, the maximum linear speed of the heart wall is
(b)
The maximum change in frequency between the sound that arrives at the wall of the baby’s heart and the sound emitted by the source.
(b)
Answer to Problem 40P
The maximum change in frequency between the sound that arrives at the wall of the baby’s heart and the sound emitted by the source is
Explanation of Solution
The frequency of the wave when the heart approaches the source at maximum velocity is given by,
Here,
The maximum change in frequency is,
Use equation (III) in (IV),
Conclusion:
Substitute
Therefore, The maximum change in frequency between the sound that arrives at the wall of the baby’s heart and the sound emitted by the source is
(c)
The maximum change in frequency between the reflected sound received by the detector and that emitted by the source.
(c)
Answer to Problem 40P
The maximum change in frequency between the reflected sound received by the detector and that emitted by the source is
Explanation of Solution
The frequency of the wave when the heart approaches the source at maximum velocity is,
Use equation (VI) for the change in frequency when the heart wall is a moving source.
Here,
Use equation (III) in equation (VII),
Solve equation (VIII) for
Conclusion:
The velocity of the source and the observer in expression (IX) refers to the movement of the heart wall, and the velocity of the sound wave is much greater than those velocities,
Substitute
Therefore, the maximum change in frequency between the reflected sound received by the detector and that emitted by the source is
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Chapter 13 Solutions
Principles of Physics: A Calculus-Based Text
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