(a)
The mass per unit length of the rope.
(a)
Answer to Problem 1SP
The mass per unit length of the rope is
Explanation of Solution
Given Info: The length of the rope is
Write the formula to calculate the mass per unit length of the rope.
Here,
m is the mass of the rope
L is the length of the rope
Substitute
Conclusion:
Therefore, the mass per unit length of the rope is
(b)
The speed of the wave on the rope.
(b)
Answer to Problem 1SP
The speed of the wave on the rope is
Explanation of Solution
Given Info: The tension on the rope is
Write the formula to calculate the speed of the wave on the rope
Here,
F is the tension on the rope
v is the speed of the wave
Substitute
Conclusion:
Therefore, the speed of the wave on the rope is
(c)
The wavelength for the wave on the rope.
(c)
Answer to Problem 1SP
The wavelength for the wave on the rope is
Explanation of Solution
Given Info: The speed of the wave is
Write the expression for the speed of the wave.
Here,
v is the speed of the wave
f is the frequency of the wave
Substitute
Conclusion:
Therefore, the longest possible wavelength is
(d)
The number of cycles of the waves.
(d)
Answer to Problem 1SP
The number of cycles of wave on the rope is
Explanation of Solution
Given Info: The length of the rope is
Write the expression to calculate the number of cycles on the rope.
Here,
n is the number of cycles on the rope
L is the length of the rope
Substitute
Conclusion:
Therefore, the number of cycles of wave on the rope is
(e)
The time required to travel the wave from one end to the other end.
(e)
Answer to Problem 1SP
The time required is
Explanation of Solution
Given Info: The length of the rope is
Write the expression to calculate the time required for the wave to travel to other end.
Here,
t is the time required for the wave for the travelling
Substitute
Conclusion:
Therefore, The time required is
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Chapter 15 Solutions
Physics of Everyday Phenomena
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