There were a few typos, so I corrected them and reposted.

Indeed, the frequencies of the musical scale are in GP, with first term 
A = a1 = 440 and the next higher A, an octave higher, is a13 = 880,
which has twice the frequency.

an = a1∙rn-1

a13 = 440∙r13-1

880 = 440∙r12

2 = r12



That's the ratio, approximately  1.059463094

So the A above middle C vibrates 400 times a second.

A-sharp (B-flat) vibrates at



we multiply by 



each time.

B vibrates at 448.9848192

C above middle C vibrates at 475.6828457

So middle C vibrates at half that

So middle C vibrates at 237.8414229  

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C)Where on the scale is a note with a Frequency of 600?





 

 



  

  

 

 



 





That's a tiny bit sharper than the 7th note of the scale
starting on A-440.

A, A#, B, C, C#, D, D#, E, F, F#,  G, G#
1,  2, 3, 4,  5, 6,  7, 8, 9, 10, 11, 12

So 600 is a bit sharper than D#, the same as Eb.

[# means sharp, b means flat]

Edwin