Concept explainers
(a)
The power transmitted by the wave as a function of
(a)
Answer to Problem 58AP
The power transmitted by the wave as a function of
Explanation of Solution
Write the expression for the power transmitted.
Here,
Write the general expression for wave function of the wave.
Here,
The derivative of the position of the wave gives velocity of the wave.
Differentiate equation (II) with respect to
The maximum velocity will be
Rewrite equation (I) by substituting
Write the expression for speed of the wave.
Here,
Conclusion:
Substitute,
Substitute,
Therefore, power transmitted by the wave as a function of
(b)
The proportionality between power and
(b)
Answer to Problem 58AP
The power transmitted is directly proportional to the square of the maximum speed of the particle.
Explanation of Solution
Write the expression for the power transmitted.
Here,
Write the general expression for wave function of the wave.
Here,
The derivative of the position of the wave gives velocity of the wave.
Differentiate equation (II) with respect to
The maximum velocity will be
Rewrite equation (I) by substituting
According to equation (VII) the power transmitted is directly proportional to square of the maximum speed.
Conclusion:
Therefore, the power transmitted is directly proportional to the Square of the maximum speed of the particle.
(c)
The energy contained in a section of string 3.00 m long as a function of
(c)
Answer to Problem 58AP
The energy contained in a section of string 3.00 m long as a function of
Explanation of Solution
Write the expression for energy in terms of power.
Here,
Write the expression for time in terms of speed and distance.
Conclusion:
Substitute,
Substitute,
Therefore, the energy contained in a section of string 3.00 m long as a function of
(d)
The energy contained in a section of string 3.00 m long as a function of mass.
(d)
Answer to Problem 58AP
The energy contained in a section of string 3.00 m long as a function of mass is
Explanation of Solution
Write the expression for kinetic energy in the string
Here,
Conclusion:
Therefore, the energy contained in a section of string 3.00 m long as a function of mass is
(e)
The energy that the wave carries past a point in
(e)
Answer to Problem 58AP
The energy that the wave carries past a point in
Explanation of Solution
Use equation (VIII) to obtain the energy carried by the wave.
Conclusion:
Substitute,
Therefore, the energy that the wave carries past a point in
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Chapter 16 Solutions
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