Question

The formula for determining the frequency, f, of a note on a piano is mc016-1.jpg, where h is the number of half-steps from the A above middle C on the keyboard. A note is six half-steps away from the A above middle C. The frequency of the A above middle C is 440 Hz. How much greater is the frequency of the new note compared with the frequency of the A above middle C?
29.3%
41.4%
70.7%
182.3%

Answer 1

Use f = 440·2^(h/12). For h = 6: f = 440·2^(6/12) = 440·2^(1/2) = 440√2.
Percent increase = (√2 − 1)·100% ≈ 0.41421356·100% ≈ 41.4%.