The highest note on a piano is C, four octaves above the middle C. Find the frequencies and wavelengths (in air) of these notes.

### 2 Answers

We need to know the speed of sound in air, which varies slightly with temperature

and density, but at sea level is about 331 meters per second. Using this value:

The frequency of the A above middle C is 440 cycles per second (or Hertz). Each

octave down reduces the frequency of the corresponding A by half, so the lowest

A on a piano has a frequency of 27.5 cycles per second. The wavelength is found

by dividing the speed of sound (331 m/sec) by the frequency, so the lowest A has

a wavelength of 331 / 27.5, or 12.036 meters.

The highest C on the piano has a frequency of 4096 cps (Hertz), so its wavelength

is 331 / 4096, or 0.08081 meter, which is the same as 8.081 centimeters.

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