Question

the musical note e can be modeled by the function, y = asin(1320πx), where a = 1 and x is the time in seconds. playing note e on your computer, you notice that it is not loud enough to be heard across the room. what change can you make to the function to make note e louder than the original? let a < 0. let a > 0. let a > 0 and a < 1. let a > 1 or a < -1.

Explanation:

Step1: Recall amplitude - loudness relationship

In a sinusoidal function $y = a\sin(bx)$, the amplitude is $|a|$. The loudness of a sound modeled by a sinusoidal function is related to the amplitude. Larger amplitude means louder sound.

Step2: Analyze the given function

The original function is $y = a\sin(1320\pi x)$ with $a = 1$. To make the note louder, we need to increase the magnitude of $a$. That is, we need $|a|>1$, which means $a > 1$ or $a<- 1$.

Answer:

Let $a>1$ or $a < - 1$.