Answer:
Option B - 41.4%
Step-by-step explanation:
Given : The formula for determining the frequency, f, of a note on a piano is [tex]f(h)=440(2)^{\frac{h}{12}}[/tex] 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.
To find : How much greater is the frequency of the new note compared with the frequency of the A above middle C?
Solution : The formula for determining the frequency [tex]f(h)=440(2)^{\frac{h}{12}}[/tex]
When the note is at initial stage i.e, h=0 frequency is
[tex]f(0)=440(2)^{\frac{0}{12}}[/tex]
[tex]f(0)=440(1)[/tex]
[tex]f(0)=440[/tex]
A note is six half-steps away from the A above middle C i.e, h=6
[tex]f(6)=440(2)^{\frac{6}{12}}[/tex]
[tex]f(6)=440(2)^\frac{1}{2}[/tex]
[tex]f(6)=440(1.41)[/tex]
[tex]f(6)=622.25[/tex]
Initial frequency is 440 hz.
Final frequency is 622.25 hz.
To find change formula is
[tex]=\frac{\text{final} - \text{initial}}{\text{Initial}}[/tex]
[tex]=\frac{622.25- 440}{440}[/tex]
[tex]=0.414[/tex]
Frequency change in percentage
[tex]0.414\times 100= 41.4\%[/tex]
Therefore, Option B is correct.
Answer:
How much greater is the frequency of the new note compared with the frequency of the A above middle C?
Step-by-step explanation:
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