Concept explainers
(a)
The power transmitted by the wave.
(a)
Answer to Problem 16.58AP
The power transmitted by the wave is
Explanation of Solution
Given info: The linear density of string is
The formula to calculate the speed of transverse wave is,
Here,
The formula to calculate maximum velocity is,
Here,
The formula to calculate power transmitted by the wave is,
Here,
Substitute
Substitute
Solve the above expression for
Conclusion:
Therefore, the power transmitted by the wave is
(b)
The proportionality relation between the power and
(b)
Answer to Problem 16.58AP
The power is directly proportional to square of the speed of the particle.
Explanation of Solution
Given info: The linear density of string is
From equation (1), the power is given as,
From the above expression it is clear that the power transmitted by the wave is directly related with the square of the speed of the particle. The more the speed of the particle the more is power transmitted.
Conclusion:
Therefore, the power is directly proportional to square times the speed of the particle.
(c)
The energy contained in contained in
(c)
Answer to Problem 16.58AP
The energy contained in
Explanation of Solution
Given info: The linear density of string is
The formula to calculate energy is,
Here,
Substitute
The formula to calculate speed is,
Substitute
Here,
Substitute
Solve the above expression for
Conclusion:
Therefore, the energy contained in
(d)
The energy in terms of mass.
(d)
Answer to Problem 16.58AP
The mass of string is
Explanation of Solution
Given info: The linear density of string is
The formula to calculate kinetic energy of string is,
Here,
The kinetic energy of string is converted to energy io the section of the string as the wave propagates through string.
Substitute
Solve the above expression for
Conclusion:
Therefore, the mass of string is
(e)
The energy carried by the wave past a point
(e)
Answer to Problem 16.58AP
The energy carried by the wave is
Explanation of Solution
Given info: The linear density of string is
The formula to calculate energy in terms of power is,
Here,
Substitute
Conclusion:
Therefore, the energy carried by the wave is
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Chapter 16 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
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