FAN AND MEDAL!
Each key on a piano produces a frequency that is 2^1/12 times higher than the frequency of the key immediately to its left. Moving "n" keys to the right of any key increases the frquency of the starting note by a factor 2^n/12. The key corresponding to Concert A has a frequency of 440 Hz. What is the frequency of note D, which is 5 keys to the right of Concert A?

Question

FAN AND MEDAL!
Each key on a piano produces a frequency that is 2^1/12 times higher than the frequency of the key immediately to its left. Moving "n" keys to the right of any key increases the frquency of the starting note by a factor 2^n/12. The key corresponding to Concert A has a frequency of 440 Hz. What is the frequency of note D, which is 5 keys to the right of Concert A?

roadjester · Answer

Is it $$2^{({n/12)}}$$ or $$2^n \over 12$$?

sophadof · Answer

@roadjester I have no idea..

sophadof · Answer

i think the first one

roadjester · Answer

You think? O.o

sophadof · Answer

yes its the first one @roadjester

briannaontimeforreal · Answer

i agree

roadjester · Answer

Okay, so to solve this, what you're going to do is this?
$$\large 2^{({n \over 12})}=440$$

Next, you're going to take the log base 2, of both sides:
$$\large {\log_2}2^{({n \over 12})}={\log_2}440$$

Doing this allows you to solve for the value of "n".

Once you find n, add 5. Then plug that number back into the original equation.

roadjester · Answer

And you're done.

sophadof · Answer

uh.. @roadjester

roadjester · Answer

I lost you?

briannaontimeforreal · Answer

im confused

sophadof · Answer

Yeh... My calculator won't do that @roadjester

roadjester · Answer

Is your calculator a scientific calculator? Need a scientific to do logarithmic calculations.

briannaontimeforreal · Answer

im confused @sophadof

sophadof · Answer

yes it is..i also did it on Mathway.com but it won't allow the $$\log_{2} 2^\frac{ n }{ 12 }$$

sophadof · Answer

it won't let me do the big 2 after the log 2 @roadjester

roadjester · Answer

umm....that's because you don't "need to". That's the nice thing about logarithmics.

$$\log_\cancel{2} \cancel{2}^{\frac n {12}}=\frac n {12}$$

roadjester · Answer

oops, missed the log part,
$$\cancel{\log_2}$$

roadjester · Answer

The "big 2" and the log base 2 will cancel out

sophadof · Answer

ok.. but then how do i figure out n? @roadjester

roadjester · Answer

multiply by 12 on both sides....
$$12 \times \log_2{440}$$

sophadof · Answer

105.3? @roadjester

roadjester · Answer

Yep
Now add 5, and that's your "new n"

sophadof · Answer

so 110.3 @roadjester (:??

roadjester · Answer

yes, now put it back into ur original equation

sophadof · Answer

okay! Thank you! @roadjester SO MUUUCH