Question

A trumpet player is tuning his instrument by playing an A note simultaneously with the first-chair trumpeter, who has perfect pitch. The first-chair player's note is exactly 440 Hz, and 2.10 beats per second are heard.What are the two possible frequencies of the other players note?

Answer 1

To develop this problem, it is necessary to apply the concepts related to Beat

The Beat is an acoustic phenomenon that is generated by two sine waves interfering with slightly different frequencies. The beat frequency is equal to the difference in the frequencies of the two original waves:

$f_{bat} = |(f_1 \pm f_B)|$

Our values are given as

$f_1 = 440Hz$

$f_B = 2.1Hz$

For the particular case we have two possible frequencies:

$1) f_{bat} = |(f_1 - f_B)|$

$f_{bat} = |(440 - 2.1)|$

$f_{bat} = 437.9Hz$

$2) f_{bat} = |(f_B + f_1)|$

$f_{bat} = |(440 +2.1)|$

$f_{bat} = 442.1Hz$

Therefore the two possibles frequencies of the other players note are 437.9Hz and 442.1Hz