Concept explainers
(a)
Rank the functions from largest to the smallest according to their amplitude.
(a)
Answer to Problem 3OQ
The ranking of functions from largest to the smallest according to their amplitude is
Explanation of Solution
Write the general expression for a sinusoidal wave.
Here,
Consider wave function (a).
Compare equation (I) and (II). The amplitude of the wave (a) is
Consider wave function (b).
Compare equation (I) and (III). The amplitude of the wave (b) is
Consider wave function (c).
Compare equation (I) and (IV). The amplitude of the wave (c) is
Consider wave function (d).
Compare equation (I) and (V). The amplitude of the wave (d) is
Consider wave function (e).
Compare equation (I) and (VI). The amplitude of the wave (e) is
Thus the raking of amplitude each wave from largest to the smallest is (c)=(d)>(e)>(b)>(a).
Conclusion:
Therefore, the ranking of wave functions from largest to the smallest according to their amplitude is
(b)
Rank the functions from largest to the smallest according to their wavelength.
(b)
Answer to Problem 3OQ
The ranking of functions from largest to the smallest according to their wavelength is
Explanation of Solution
Write the expression for wavelength.
Conclusion:
Substitute,
Substitute,
Substitute,
Substitute,
Substitute,
Thus, the ranking of wavelength from larger to smaller is (c)>(a)=(b)>(d)>(e).
Therefore, the ranking of functions from largest to the smallest according to their wavelength is
(c)
Rank the functions from largest to the smallest according to their frequencies.
(c)
Answer to Problem 3OQ
The ranking of functions from largest to the smallest according to their frequency is
Explanation of Solution
Write the expression for frequency.
Conclusion:
Substitute,
Substitute,
Substitute,
Substitute,
Substitute,
Thus, the ranking of frequencies of wave from largest to smallest is (e)>(d)>(a)=(b)=(c).
Therefore, the ranking of functions from largest to the smallest according to their frequency is
(d)
Rank the functions from largest to the smallest according to their period.
(d)
Answer to Problem 3OQ
The ranking of functions from largest to the smallest according to their period is
Explanation of Solution
Write the expression for period.
Conclusion:
Since frequency is inversely proportional to time period, the ranking will be the reverse order of the ranking in part (c).
Thus, the ranking of functions from largest to the smallest according to their period is
Therefore, the ranking of functions from largest to the smallest according to their period is
(e)
Rank the functions from largest to the smallest according to their speed.
(e)
Answer to Problem 3OQ
The ranking of functions from largest to the smallest according to their speed is
Explanation of Solution
Write the expression for speed.
Conclusion:
Substitute,
Substitute,
Substitute,
Substitute,
Substitute,
Thus, the ranking of speed of the wave from largest to smallest is (c)>(a)=(b)=(d)>(e).
Therefore, ranking of functions from largest to the smallest according to their speed is
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