ALGEBRA 2- Exam 10 continued The pitch of a musical note is determined by its fr

Question

ALGEBRA 2- Exam 10 continued The pitch of a musical note is determined by its frequency in Hertz. The trigo s determined by its frequency in Hertz. The trigonometric function = a sin approximates the sound of a note with volume a, frequer t seconds. volume where a = 1 e a, frequency f, and a duration of For the purposes of the following problems, we wil assume all pitches are played at a Within a major scale, the frequencies of the notes maintain c scale. The first note to the third note have a frequency ratio of 4:5, the first to the first to seventh a ratio of 8:15, and the first to the octave (eigh Below, you will see the graph of the standard pitch, A at 440Hz in black, alongside another pitch in grey as well as the eight notes of an octave of the A major scale with their pitch names ertain ratios to the first note of the fifth a ratio of 2:3 th) a ratio of 1:2 I hate BC# D E F# G# A 32. Give the equation, p(), for the function in grey and identify w 32. Give the equation, p(t), for the function in grey and identify which pitch it is. The note is and can be modeled by p(t) 33. Find the equation, p(t), for C# and add its graph to the graph of A440 below C# can be modeled by p(t) = FILL IN YOUR NAME AND THE OTHER REQUIRED INFORMATION ON EACH PAGE OF THE EXAM AND MAIL THE EXAM TO THE SCHOOL 80

Explanation / Answer

lets denote each small square block be of a time duration T.

then time taken for a complete wave for A=6*T (it covers 6 small blocks)

frequency =1/(6*T)

it is given that frequency=440 Hz

==>T=3.7878*10^(-4)

time taken by the gray curve=4*T

frequency will be 1/(4*T)=660 Hz

A is the first note.

with first note, this gray curve has 3:2 ratio in terms of frequency.

as per the information, it is E note.

and it can be modeled with f=660 Hz as

p(t)=1*sin(2*pi*660*t)

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