Question

Musicians can use beats to tune their instruments. One flute is properly tuned and plays the musical note A at exactly 440 Hz. A second player sounds the same note and hears that her instrument is slightly "flat" (that is, at too low a frequency). Playing at the same time as the first flute, she hears three loud-soft-loud beats per second.

What is the frequency of her instrument?

Answer 1

Solution:

Frequency of the beat to tune the instrument is, \(\mathrm{f}_{\text {beat }}=3\)

Frequency of the musical note from flute is, \(\mathrm{f}_{\text {musical note }}=440 \mathrm{~Hz}\)

Frequency of the flat notes heard by the second player is, \(\mathrm{f}_{\text {flat }}\)

$$ \begin{aligned} \mathrm{f}_{\text {beat }} &=\mathrm{f}_{\text {musical note }}-\mathrm{f}_{\text {instrument }} \\ \quad 3 &=440 \mathrm{~Hz}-\mathrm{f}_{\text {instrument }} \\ \mathrm{f}_{\text {instrument }} &=440-3 \\ &=437 \mathrm{~Hz} \end{aligned} $$

One flute is more than enough for this situation.

Therefore the frequency of her instrument is \(\mathrm{f}=437 \mathrm{~Hz}\).