Question

The formula for determining the frequency, f, of a note on a piano is f=440(2)^h/12 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?

A)29.3%
B)41.4%
C)70.7%
D)182.3%

Answer 1

i think it is c

Explanation:

Answer 2

41.4%

Explanation:

The formula for determining the frequency:
`f(h)=440(2)^{(h)/(12)}` --A

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.

Now we are supposed to find How much greater is the frequency of the new note compared with the frequency of the A above middle C?

Now initially there is no half steps .

So, substitute h =0

`f(0)=440(2)^{(0)/(12)}`

`f(0)=440`

Now we are given that A note is six half-steps away from the A above middle C

So, substitute h =6

`f(6)=440(2)^{(6)/(12)}`

`f(6)=622.25`

Now To find change percentage

Formula:
`=\frac{\text{final} - \text{initial}}{\text{Initial}} * 100`

`=(622.25- 440)/(440) * 100`

`=0.414 * 100`

`=41.4\%`

Hence the frequency of the new note is 41.4% greater with the frequency of the A above middle C.