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?
Choose the correct choice from the following:
A) 440
B) 440 * sqrt (2)
C) 400 * sqrt (3)
D) 450 * sqrt (4)
E) 440 * sqrt (5)
let the constant be k   F1 = 440   F2 = 440k   F3 = 440 k * k = 440 * k^2   F13= 440 * k^12   we know F13 = 2 *F1 = 2 * 440 2 * 1= 
<gadget id="calculator">2 * 1</gadget>
<output>2</output>
2 * 440= 
<gadget id="calculator">2 * 440</gadget>
<output>880</output>
880   880/440= k^12   k = twelfth root of 2   for F7...   F7 = 440 * k^6 ( as we wrote for F2 and F3)   F7 = 440 * (twelfth root of 2) ^ 6   F7 = 440 * sqrt (2)   Answer 440 * sqrt (2)
<result>B</result>
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?