# The lowest note on a piano is A, four octaves below the A.?

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

• 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.

Source(s): I have studied both music and physics