The first key on a piano keyboard corresponds to a pitch with a frequency of 27.5 cycles per second. With every successive key, going up the black and white keys, the pitch multiplies by a constant. The formula for the frequency of the pitch sounded when the nth note up the keyboard is played is given by log _(2)((f)/(27.5))

Question

The first key on a piano keyboard corresponds to a pitch with a frequency of 27.5 cycles per second. With every successive key, going up the black and white keys, the pitch multiplies by a constant. The formula for the frequency of the pitch sounded when the nth note up the keyboard is played is given by log _(2)((f)/(27.5))

A. a note has a frequency of 830 cycles per second. How many notes up the piano keyboard is this?

Answer 1

I do not really understand the question but all I can say is:

geometric sequence
fn = a r^(n-1)
fn = 27.5 r^(n-1)
log ( fn /27.5)= (n-1) log r

Answer 2

Not familiar with your formula, but here is another way to look

at the frequencies of the piano keys

when f(n) is the frequency of a certain key n
it can be found by
f(n) = 440* 2^( (n-49)/12 )

or

if you take log (f(n)) - log (f(n-1)), where n is the key number on the piano,
you get a constant 0.025085832

440* 2^( (n-49)/12 ) = 830
2^(n-49)/12 = 1.8863636..
((n-49)/12) log2 = log 1.8863636..
(n-49)/12 = .915607812
n-49 = 10.98729375
n = 59.987 , looks like the key # 60 on the piano

According to a chart of frequencies, there is no key with a frequency of exactly 830.

www.askinglot.com/open-detail/609252

Answer 3

To find out how many notes up the piano keyboard have a frequency of 830 cycles per second, we can use the given formula:

log_(2)((f)/(27.5)) = n

Here, f represents the frequency of the note we want to find, which is 830 cycles per second.

Substituting the values into the formula, we have:

log_(2)((830)/(27.5)) = n

Using logarithmic properties, we can simplify this equation:

log_(2)((830)/(27.5)) = log_(2)(830) - log_(2)(27.5)

Now, we can calculate the logarithms using a calculator:

n ≈ log_(2)(830) - log_(2)(27.5) ≈ 6.699 - 4.807 ≈ 1.892

Therefore, the note with a frequency of 830 cycles per second is approximately 1.892 notes up the piano keyboard.

Answer 4

To find out how many notes up the piano keyboard a frequency of 830 cycles per second corresponds to, we can use the given formula:

n = log₂(f / 27.5)

where:
- n represents the number of notes up the piano keyboard
- f represents the frequency of the note in cycles per second (in this case, 830)

Let's plug in the values and solve for n.

n = log₂(830 / 27.5)

To evaluate this logarithm, you can use a scientific calculator or an online logarithm calculator. Plug in the values and calculate the result. The result will be the value of n, which represents the number of notes up the piano keyboard.

After solving the equation, the result for n turns out to be approximately 4.91. Since we can't have a fraction of a note, we round up to the nearest whole number. Therefore, the note with a frequency of 830 cycles per second is approximately 5 notes up the piano keyboard.