Concept explainers
(a)
The maximum speed of an element of air in the sound wave.
(a)
Answer to Problem 63P
The maximum speed of an element of air in the sound wave is
Explanation of Solution
Write the expression for the intensity of the sound.
Here,
Write the equation for
Here,
Put the above equation in equation (I).
Write the equation for the maximum speed of the sound.
Here,
Put the above equation in equation (II) and rewrite it for
Conclusion:
Given that the intensity of the sound is
Substitute
Therefore, the maximum speed of an element of air in the sound wave is
(b)
The average kinetic energy of the eardrum.
(b)
Answer to Problem 63P
The average kinetic energy of the eardrum is
Explanation of Solution
Write the equation for the average kinetic energy.
Here,
Write the equation for
Here,
Put the above equation in equation (IV).
Conclusion:
Given that the mass of the eardrum is
Substitute
Therefore, the observed frequency if the source and observer are moving away from each other is
(c)
Comparison of the average kinetic energy of the eardrum due to collisions with air molecules in the absence of sound wave with result of part (b).
(c)
Answer to Problem 63P
The average kinetic energy of the eardrum with collisions with air molecules in the presence of sound wave at the threshold human hearing is of the order of ten times that it can be in the absence of a sound wave.
Explanation of Solution
Write the value of average kinetic energy of the eardrum due to collisions with air molecules in the absence of sound wave.
Here,
Conclusion:
Comparison of
Therefore, the average kinetic energy of the eardrum with collisions with air molecules in the presence of sound wave at the threshold human hearing is of the order of ten times that it can be in the absence of a sound wave.
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