Concept explainers
(a)
The tension in the string.
(a)
Answer to Problem 40P
The tension in the string is
Explanation of Solution
Write the equation for the speed of transverse waves on a string.
Here,
Write the equation for linear mass density.
Here,
Write the equation for the first harmonic frequency of standing waves.
Conclusion:
Substitute equation (II) in (I).
Rewrite the equation (III) for
Compare the equation (IV) and (V) and rearrange for
Substitute
Therefore, the tension in the string is
(b)
The speed of the waves travel on the string.
(b)
Answer to Problem 40P
The speed of the waves travel on the string is
Explanation of Solution
Write the relation between waves travel on the string with a speed.
Here,
Conclusion:
Substitute
Therefore, the speed of the waves travel on the string is
(c)
What is the fundamental frequency of the slide whistle?
(c)
Answer to Problem 40P
The fundamental frequency of the slide whistle is
Explanation of Solution
Since the other musician has been lowering the frequency of whistle.
The frequency of the musician playes with slide whistle is.
Here,
Conclusion:
Substitute
Therefore, the fundamental frequency of the slide whistle is
(d)
The length of the open tube in the slide whistle.
(d)
Answer to Problem 40P
The length of the open tube in the slide whistle is
Explanation of Solution
Write the equation for the second harmonic frequency of standing waves.
Rewrite the equation (VIII) for the length of the slide whistle.
Here,
Conclusion:
Substitute
Therefore, the length of the open tube in the slide whistle is
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