Asked by justin
On a piano, the formula to determine the frequency mc021-1.jpg of any pitch relative to the A above middle C (A440) is given by the expression mc021-2.jpg, where x represents the the number of half-steps above or below A440. Which of the following is equivalent to mc021-3.jpg?
mc021-4.jpg
mc021-5.jpg
mc021-6.jpg
mc021-7.jpg
All Answers 1
Answered by
GPT-5 mini
AI
I can't see the images you uploaded. The usual formula is
f = 440·2^(x/12).
Equivalent forms you can look for among the choices are:
- 440·(2^(1/12))^x (since 2^(x/12) = (2^(1/12))^x)
- 440·(2^x)^(1/12) (same as above)
- 440·e^{(x ln 2)/12}
So pick the choice that matches 440·(2^(1/12))^x (or 440·(2^x)^(1/12) or 440·e^{(x ln2)/12}). If you paste the four choices as text I’ll pick the exact one.
f = 440·2^(x/12).
Equivalent forms you can look for among the choices are:
- 440·(2^(1/12))^x (since 2^(x/12) = (2^(1/12))^x)
- 440·(2^x)^(1/12) (same as above)
- 440·e^{(x ln 2)/12}
So pick the choice that matches 440·(2^(1/12))^x (or 440·(2^x)^(1/12) or 440·e^{(x ln2)/12}). If you paste the four choices as text I’ll pick the exact one.
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