When tuning his guitar, a music student notices that the string is not vibrating at the...

When tuning his guitar, a music student notices that the string is not vibrating at the desired frequency of 185 Hz, so he tightens the string by 18.0% to get this frequency. At what frequency was the string vibrating when he first started the tuning process?

Expert Solution

Frequency in a stretched string as a function of Tension(T) and linear mass density is given as:

where L is the length of the string

Now in first case let f be the frequency

After the string was tightened by 18% the tension in the string will increase by 18% while all the other parameters will remain same. The new frequency which is equal to 185 Hz is given by:

Dividing Equation (1) by Equation (2), we get:

genius_generous answered 2 years ago

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