Question

1) In this scale, the frequency of each C-note in vibrations per second is measured in Hz. It can be expressed as a power of 2, as shown. What is the frequency of the note C7 in exponential form and in logarithmic form?
C4: 256 Hz
C5: 512 Hz
C6: 1024 Hz

2) If the frequency of a note C is 32 vibrations per second, how many octaves higher or lower than middle C is this note?

A) 3 octaves lower
B) 4 octaves higher
C)2 octaves higher
D)1 octaves lower

Answer 1

What is C7 in decimal? Once you obtain this then you just ask yourself

2^x = C7

For example, with C4, 2^x = 256
x = 8 so
C4 = 256 = log_2 (256)

In exponential, 256 = \[2^{8}\]

In logarithmic

\[\log_{2} (256) = 8\]

What goes on the right hand side of a log formula is equivalent to the power in the exponent.

Answer 2

2^11= 2048 Hz; log2 2048 = 11 Thats what I got for question one but I can't figure out number 2