Concept explainers
(a)
The number of loops exhibit in the pattern.
(a)
Answer to Problem 33P
The number of loops exhibit in the pattern is
Explanation of Solution
The expression for given wave function is,
Here,
Compare the above equation with standard wave function.
Here,
Write the expression for wave number.
Here,
Write the expression for angular frequency.
Here,
Write the expression for distance between adjacent nodes.
Write the expression for number of loops formed on the string.
Here,
Conclusion:
Substitute
Substitute
Substitute
Substitute
Therefore, the number of loops exhibit in the pattern is
(b)
The fundamental frequency of vibration.
(b)
Answer to Problem 33P
The fundamental frequency of vibration is
Explanation of Solution
Write the expression for speed of the wave.
Write the expression for wavelength of the standing wave vibration.
Here,
Write the expression for fundamental frequency.
Here,
Conclusion:
Substitute
Substitute
Substitute
Therefore, the fundamental frequency of vibration is
(c)
The number of loops are present in the new pattern.
(c)
Answer to Problem 33P
The number of loops are present in the new pattern is one loop.
Explanation of Solution
Write the expression for tension in the string.
Here,
Write the expression for tension increases in the string.
Write the expression for constant wavelength.
Here,
Write the expression for wavelength of the standing wave vibration.
Here,
Conclusion:
Substitute
Substitute
Substitute
Hence, one loop formed in the string.
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Chapter 18 Solutions
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