Question

when tuning his guitar, a music student notices that the string is not vibrating at the desired frequency of 195 hz, so he tightens the string by 16.4% to get this frequency. at what frequency was the string vibrating when he first started the tuning process?

Answer 1

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 = $\frac{1}{2L}$ $\sqrt{\frac{T}{} }$μ

where L is the length of string

Now in first case let f be the frequency

f = $\frac{1}{2L}$ $\sqrt{\frac{T}{} }$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 = $\frac{1}{2L}$ $\sqrt{1.164T$ /  μ

⇒ 195 = $\frac{1}{2L}$ $\sqrt{1.164T}$/μ                      (ii)

Dividing equation (i) by equation (ii), we get;

⇒$\frac{f}{195}$ = $\sqrt{\frac{T}{1.164T} }$

⇒f = 195 $\sqrt{\frac{1}{1.164} }$

⇒ 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

#SPJ4