Musicians can use beats to tune their instruments. One flute is properly tuned and plays the...

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?

Expert Solution

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 $\mathrm{f}=437 \mathrm{~Hz}$.

genius_generous answered 2 years ago

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