Question

In certain ranges of a piano keyboard, more than one string is tuned to the same note to provide greater intensity. for example, the note at 112 hz has two strings at this pitch. if one string slips from its normal tension of 607 n to 515 n, what beat frequency will be heard when the two strings are struck simultaneously? answer in units of beats/s

Answer 1

The pitch is proportional to the square root of the tension, so the detuning coefficient is


`k = √(515/607)\approx0.921`

The detuned string now has the frequency

`f' = 112k \approx 103\text{ Hz}`

Thus, the beat frequency is now calculated as usual - it is a difference between these two frequencies


`f_b = 112-103 = 9\text{ beats/s}`