Concept explainers
(a)
Maximum transverse displacement of the rope if
(a)
Answer to Problem 66PQ
The maximum transverse displacement of the rope if
Explanation of Solution
Write the general equation for the standing wave formed when two waves travelling in opposite direction superimposes each other.
Here,
Write the equation for the first wave function taking part in super position.
Write the equation for the second wave function taking part in super position.
Both the waves are travelling in the opposite direction. So after the overlap the resultant displacement is equal to the sum of displacements of individual waves.
Add equations (II) and (III) to get the resultant amplitude of the wave.
Substitute equations (II) and (III) in (IV).
For maximum value of
Rewrite equation (V) to get maximum displacement if
Here,
Conclusion:
Substitute
Therefore, the maximum transverse displacement of the rope if
(b)
Maximum transverse displacement of the rope if
(b)
Answer to Problem 66PQ
The maximum transverse displacement of the rope if
Explanation of Solution
Rewrite equation (V) to get maximum displacement if
Here,
Conclusion:
Substitute
Therefore, the maximum transverse displacement of the rope if
(c)
Location of the first three antinodes on the rope.
(c)
Answer to Problem 66PQ
The first antinode is located at
Explanation of Solution
Write the condition for occurrence of antinodes in the given wave.
Here,
Rearrange equation (V) to find
Here,
Rearrange equation (V) to find
Here,
Rearrange equation (V) to find
Here,
Conclusion:
Substitute
Substitute
Substitute
Therefore, the first antinode is located at
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Chapter 18 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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