Sound problems related to music

Wave questions II

Consider the musical note G, 392 Hz.  Find the following:

1.  The frequencies of the next two G's, one and two octaves above.

2.  The frequency of the G one octave lower than 392 Hz.

3.  The frequency of G#, one semi-tone (piano key or guitar fret) above this G.

4.  The frequency of A#, 3 semi-tones above G.

5.  The wavelength of the 392 Hz sound wave, assuming that the speed of sound is 340 m/s.

answers:

1.  392 x 2 = 784 Hz; 392 x 4 = 1568 Hz

2.  392/2 = 196 Hz

3.  392 x 1.0594 = 415 Hz

4.  392 x 1.0594 x 1.0594 x 1.0594  (or 392 x 1.0594^3) = 466 Hz

5.  wavelength = speed / frequency = 340/392 = 0.87 m