Concept explainers
(a)
The upper limit of hearing of elephants and rats.
(a)
Answer to Problem 60E
The upper limit of hearing of elephants is
Explanation of Solution
Write the expression for separation between ears.
Express the above relation in equation form.
Rearrange the above expression in terms of
Here,
Write the expression for wavelength of sound.
Here,
The separation between ears must be equal to the wavelength of sound that a human ear perceives; it means
Substitute
Rearrange the above expression in terms of
Conclusion:
For humans:
Substitute
Substitute
For elephants:
Substitute
Substitute
For rats:
Substitute
Substitute
Thus, the upper limit of hearing of elephants is
(b)
The experimental scaling exponent for upper limit frequency versus mass.
(b)
Answer to Problem 60E
The experimental scaling exponent for upper limit frequency versus mass is
Explanation of Solution
Write the expression for upper hearing limit.
Here,
Express the above relation in ratio for two mammals.
Here, subscript1 is used for first mammal and subscript2 is used for second mammals.
Apply logarithm on both sides in above expression.
Rearrange the above expression in terms of
Conclusion:
Substitute
Thus, experimental scaling exponent for upper limit frequency versus mass is
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Chapter 22 Solutions
General Physics, 2nd Edition
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