
Concept explainers
(a)
Whether the maximum velocity and the greatest acceleration of the eardrum are for high-frequency sounds or low-frequency sounds for a given vibration amplitude.
(a)

Answer to Problem 40P
The maximum velocity and the greatest acceleration of the eardrum are for high-frequency sounds for a given vibration amplitude.
Explanation of Solution
Write the expression for the maximum velocity.
Here,
Write the expression for
Here,
Put equation (II) in equation (I).
Equation (III) implies that
Write the expression for the maximum acceleration.
Here,
Put equation (II) in equation (IV).
Equation (V) implies that
Conclusion:
Since maximum velocity is proportional to frequency and the maximum acceleration is proportional to square of the frequency, maximum velocity and acceleration will occur for high frequency sounds.
Therefore, the maximum velocity and the greatest acceleration of the eardrum are for high-frequency sounds for a given vibration amplitude.
(b)
The maximum velocity and acceleration of the eardrum for vibrations of amplitude
(b)

Answer to Problem 40P
The maximum velocity of the eardrum for vibrations of amplitude
Explanation of Solution
Equation (III) can be used to find the maximum velocity and equation (V) can be used to find the maximum acceleration.
Conclusion:
Substitute
Substitute
Therefore, the maximum velocity of the eardrum for vibrations of amplitude
(c)
The maximum velocity and acceleration of the eardrum for vibrations of amplitude
(c)

Answer to Problem 40P
The maximum velocity of the eardrum for vibrations of amplitude
Explanation of Solution
Equation (III) can be used to find the maximum velocity and equation (V) can be used to find the maximum acceleration.
Conclusion:
Substitute
Substitute
Therefore, the maximum velocity of the eardrum for vibrations of amplitude
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