Question

While attempting to tune the note C at 523 Hz, a piano tuner hears 2.00 beats/s between a reference oscillator and the string. (a) What are the possible frequencies of the string

Answer 1

525 Hz and 521 Hz

Step-by-step explanation:

The possible frequencies of the string can be found by

`B = f_(0) + f_(1)\\B = f_(0) - f_(1)`

Where B is beats/sec and f0 = 523 Hz is the fundamental frequency and f1 is to be found

`f_(1)= f_(0) + B\\f_(1)= f_(0) - B`

`f_(1)= 523 + 2\\f_(1)= 523 - 2`

`f_(1)= 525\\f_(1)= 521`

Hence the possible frequencies of the string are 525 Hz and 521 Hz

Answer 2

The possible frequencies are 525 Hz and 521 Hz

Step-by-step explanation:

A string must be tune in the same frequency with the note to eliminate beats.

Given;

Frequency of note C = 523 Hz

The frequency that the piano is been tune to = 523 Hz

The beat frequency heard = 2 beats /s.

The frequencies that must have been heard can be an addition of the beat or the reduction of the beat added to the string frequency.

Frequencies of the string = ± 523 Hz

= 521 Hz or 525 Hz

Therefore the frequencies of the string are 523 Hz and 521 Hz