Concept explainers
(a)
To Find: The wave speed and tension in the string
(a)
Answer to Problem 75GP
Explanation of Solution
Given:
Length of violin
Fundamental frequency
Mass per unit length
Formula used:
Calculation:
Fundamental frequency has 2 nodes at the end and one anti-node in the middle, vibrating length of the string is 2l, so, the speed becomes
The wave speed is 281.6 m/s.
Now, find the tension in the string, T
The tension in the string is
Conclusion:
The wave speed and the tension in the string is
(b)
To Find: The length of the tube of a simple wind instrument close at one end
(b)
Answer to Problem 75GP
Explanation of Solution
Given:
Fundamental frequency
Mass per unit length
Speed of the sound
Formula used:
Calculation:
The fundamental frequency is
The tube is closed, so the frequency calculated as
The length of the tube is
Conclusion:
The length of the tube is
(c)
To Find: The frequency of first overtone of each instrument.
(c)
Answer to Problem 75GP
For Violin,
For string,
Explanation of Solution
Given:
Fundamental frequency
Speed of the sound
Formula used:
Calculation:
To determine the frequency of first overtone at each instrument, use the following equations.
It is to be known that,
For Violin,
For String,
Conclusion:
The frequency of overtone of a violin and the string are
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