Concept explainers
(a)
The linear mass density of the cord.
(a)
Answer to Problem 28P
The linear mass density of the cord is
Explanation of Solution
Find the wavelength for standing waves of the 6 loops.
Here,
Rearrange the above equation for
Write the relation between frequency, wavelength and velocity.
Here,
Find the expression for tension in the string.
Here,
Write the expression for speed of the wave in the string.
Here,
Rearrange the above equation for
Conclusion:
Substitute
Substitute
Substitute
Substitute
Therefore, the linear mass density of the cord is
(b)
The number of loops, if mass changed to
(b)
Answer to Problem 28P
The number of loops formed is
Explanation of Solution
From the equation (III) find the tension in the cord.
Write the expression for speed of the wave in the string.
Write the expression for wavelength.
Find the number of loop formed in the cord.
Conclusion:
Substitute
Substitute
Substitute
Substitute
Therefore, the number of loops formed is
(c)
The number of loops, if mass changed to
(c)
Answer to Problem 28P
The number of loops does not formed, because standing wave not formed.
Explanation of Solution
From the equation (III) find the tension in the cord.
Write the expression for speed of the wave in the string.
Write the expression for wavelength.
Find the number of loop formed in the cord.
Conclusion:
Substitute
Substitute
Substitute
Substitute
Hence, it is not an integer. So loops does not formed.
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Chapter 18 Solutions
Physics for Scientists and Engineers with Modern Physics Technology Update
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