Question

use the model y = a sin (bt), where a is the amplitude of the sound, t is time, and b is the frequency of the note to write equations for sounds having the following characteristics. since a = the volume of the note, let a = 5 for these exercises. then, use your graphing calculator to sketch a drawing of the resulting sound wave for problems 21 to 24. 21. frequency of the note a = 220 hz 22. frequency of the note f# = 185 hz

Explanation:

Step1: Recall the formula

The formula is $y = A\sin(Bt)$, where $A$ is amplitude and $B$ is related to frequency.

Step2: Determine the value of $A$

Given $A = 5$.

Step3: Relate $B$ to frequency

The relationship between angular - frequency $B$ and frequency $f$ is $B = 2\pi f$.

Step4: Write the equation for note A

For note A with $f = 220$ Hz, $B=2\pi\times220 = 440\pi$. The equation is $y = 5\sin(440\pi t)$.

Step5: Write the equation for note $F^{\#}$

For note $F^{\#}$ with $f = 185$ Hz, $B = 2\pi\times185=370\pi$. The equation is $y = 5\sin(370\pi t)$.

Answer:

For note A: $y = 5\sin(440\pi t)$
For note $F^{\#}$: $y = 5\sin(370\pi t)$