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A certain musical scale has has 13 notes, each having a

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Re: A certain musical scale has has 13 notes, each having a [#permalink]

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New post 26 Jul 2013, 05:50
Bunuel wrote:
dasikasuneel wrote:
Pushpinder wrote:
A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant. If the lowest frequency is 440 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?

A. 440 * sqrt 2
B. 440 * sqrt (2^7)
C. 440 * sqrt (2^12)
D. 440 * the twelfth root of (2^7)
E. 440 * the seventh root of (2^12)

Lowest frequency = 440
Highest frequency = 880
Lowest frequency (n) ^12 = Highest frequency
N^12 = 2 ---------------- 1
7th note = Lowest Frequency x (n)^6
7th note = 440 x (2)^6/12

Hence the answer is A


Pushpinder Ji I couldn't understand from here. Can u tell me please


1st = \(440\)
2nd = \(440k\)
3rd = \(440k^2\)
...
7th = \(440k^6\)
...
13th = \(440k^{12}=2*440=880\) --> \(440k^{12}=880\) --> \(k^{12}=2\) --> \(k=\sqrt[12]{2}\).

Thus, 7th = \(440k^6=440(\sqrt[12]{2})^6=440\sqrt{2}\).

Answer: A.

Hope it's clear.



Hi Bunuel ,

It says that the ratio of ratio of a frequency to the next higher frequency is a fixed constant.
Doesnt that mean f1/f2 = k ??

Just a little lost.

Cheers
HeirApparent.

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Re: A certain musical scale has has 13 notes, each having a [#permalink]

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New post 26 Jul 2013, 06:40
heirapparent wrote:
Bunuel wrote:
dasikasuneel wrote:
Pushpinder Ji I couldn't understand from here. Can u tell me please


1st = \(440\)
2nd = \(440k\)
3rd = \(440k^2\)
...
7th = \(440k^6\)
...
13th = \(440k^{12}=2*440=880\) --> \(440k^{12}=880\) --> \(k^{12}=2\) --> \(k=\sqrt[12]{2}\).

Thus, 7th = \(440k^6=440(\sqrt[12]{2})^6=440\sqrt{2}\).

Answer: A.

Hope it's clear.



Hi Bunuel ,

It says that the ratio of ratio of a frequency to the next higher frequency is a fixed constant.
Doesnt that mean f1/f2 = k ??

Just a little lost.

Cheers
HeirApparent.


Does not matter how you write: f1/f2=constant --> f2/f1=1/constant.
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Re: A certain musical scale has has 13 notes, each having a [#permalink]

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New post 26 Jul 2013, 08:27
Hi Bunuel ,

It says that the ratio of ratio of a frequency to the next higher frequency is a fixed constant.
Doesnt that mean f1/f2 = k ??

Just a little lost.

Cheers
HeirApparent.[/quote]

Does not matter how you write: f1/f2=constant --> f2/f1=1/constant.[/quote]

Got it ...

Cheers

HA

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Re: A certain musical scale has has 13 notes, each having a [#permalink]

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New post 24 Sep 2013, 20:12
In a geometric progression, the median is the geometric mean given by SQRT (First * Last).
Here, First is 440, Last is 2*440 = 880 and 7th Note is the median, so it's value = SQRT (440*880) = SQRT (440*440*2) = 440*SQRT(2)
A is correct.

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Re: A certain musical scale has has 13 notes, each having a [#permalink]

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Re: A certain musical scale has has 13 notes, each having a [#permalink]

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New post 27 Apr 2016, 09:26
Is this an exponential growth problem? (Since we used the y(t)=y(0)*k^t formula). Also does someone have a link to similar questions for practice? Any help will be greatly appreciated, Thank you.

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Re: A certain musical scale has has 13 notes, each having a [#permalink]

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New post 07 Sep 2017, 08:31
Hello ,

This is the solution if we take f1/f2=k

Given: f1= 440, f 13 =2(440)=880

Also f1/f2 =f2/f3 =f3/f4 =f4/f5 =f5/f6 =f6/f7 =f7/f8 =f8/f9 =f9/f10 =f10/f11 =f11/f12 =f12/f13 = K ( Some constant)

need to find f7?

we can write f2/f1= 1/k
Acc to GP fn= f1(1/k)^n-1
Then f7= 440(1/k)^6

and f13= 440(1/k)^12

880=440 (1/k)^12
(1/k)^12= 2

{(1/K)^6}^2= 2 or
(1/k)^6= √ ( 2)

Substitute the value of (1/k)^6 in equation

So f7= 440√ 2

@Banuel is this also a correct approach.

Choice A
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Re: A certain musical scale has has 13 notes, each having a [#permalink]

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New post 07 Sep 2017, 10:42
The sequence is in GP a= 440
Ar^n-1 =term of GP
Now 2ar^1-1 = ar^13-1
2= r^12--------------------1
7th term = ar^6
440*root(2)

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Re: A certain musical scale has has 13 notes, each having a   [#permalink] 07 Sep 2017, 10:42

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