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Sagot :
When he started the tuning process the string vibrating frequency was 180Hz.
Frequency in a stretched string as a function of Tension(T) and linear mass density μ is given as:
f = [tex]\frac{1}{2L}[/tex] [tex]\sqrt{\frac{T}{} }[/tex]μ
where L is the length of string
Now in first case let f be the frequency
f = [tex]\frac{1}{2L}[/tex] [tex]\sqrt{\frac{T}{} }[/tex]μ (i)
After the string was tightened by 16.4% the tension in string will increase by 16.4% while all the other parameter will remain same. The new frequency which is equal to 195Hz is given by:
⇒ f₂ = 195 = [tex]\frac{1}{2L}[/tex] [tex]\sqrt{1.164T[/tex] / μ
⇒ 195 = [tex]\frac{1}{2L}[/tex] [tex]\sqrt{1.164T}[/tex]/μ (ii)
Dividing equation (i) by equation (ii), we get;
⇒[tex]\frac{f}{195}[/tex] = [tex]\sqrt{\frac{T}{1.164T} }[/tex]
⇒f = 195 [tex]\sqrt{\frac{1}{1.164} }[/tex]
⇒ f ≈ 180Hz
What is a string's natural frequency?
The length, mass, and degree of stretching a string is used to calculate its natural frequency. Giving a system a brief shock and seeing (or listening to) its reaction is the quickest technique to establish its natural frequency.
To know more about string frequency visit:
https://brainly.com/question/14934019
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