It is currently 15 Jan 2018, 23:59

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A certain musical scale has has 13 notes, each having a different freq

Author Message
TAGS:

### Hide Tags

Intern
Joined: 17 Jul 2013
Posts: 6

Kudos [?]: 6 [0], given: 7

Location: United States
Concentration: Operations, Strategy
GPA: 3.18
WE: Engineering (Telecommunications)
Re: A certain musical scale has has 13 notes, each having a different freq [#permalink]

### Show Tags

26 Jul 2013, 04:50
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

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 = $$440k^6=440(\sqrt[12]{2})^6=440\sqrt{2}$$.

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.

Kudos [?]: 6 [0], given: 7

Math Expert
Joined: 02 Sep 2009
Posts: 43292

Kudos [?]: 139136 [0], given: 12776

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

### Show Tags

26 Jul 2013, 05:40
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 = $$440k^6=440(\sqrt[12]{2})^6=440\sqrt{2}$$.

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.
_________________

Kudos [?]: 139136 [0], given: 12776

Intern
Joined: 02 Mar 2010
Posts: 19

Kudos [?]: 18 [0], given: 16

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

### Show Tags

24 Sep 2013, 19:12
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.

Kudos [?]: 18 [0], given: 16

Intern
Joined: 14 Oct 2016
Posts: 30

Kudos [?]: 8 [0], given: 147

Location: India
WE: Sales (Energy and Utilities)
Re: A certain musical scale has has 13 notes, each having a different freq [#permalink]

### Show Tags

07 Sep 2017, 07:31
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
_________________

Abhimanyu

Kudos [?]: 8 [0], given: 147

Director
Joined: 14 Nov 2014
Posts: 633

Kudos [?]: 116 [0], given: 47

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

### Show Tags

07 Sep 2017, 09:42
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)

Kudos [?]: 116 [0], given: 47

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1820

Kudos [?]: 1043 [0], given: 5

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

### Show Tags

11 Dec 2017, 17:17
stoolfi 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)

We are given that a certain musical scale has 13 notes, ordered from least to greatest. We also know that each next higher frequency is equal to the preceding frequency multiplied by some constant. Since the first frequency is 440 cycles per second, the second frequency is 440k, the third is 440k^2, the fourth is 440k^3…the seventh frequency is 440k^6, and the thirteenth frequency is 440k^12.

Since the highest frequency is twice the lowest, we can create the following equation:

440 x 2 = 440k^12

2 = k^12

(^12)√2 = k

Thus, the seventh frequency is 440((^12)√2)^6 = 440√2.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 1043 [0], given: 5

Re: A certain musical scale has has 13 notes, each having a different freq   [#permalink] 11 Dec 2017, 17:17

Go to page   Previous    1   2   [ 26 posts ]

Display posts from previous: Sort by