Question

.Consider the following sine wave: s(t) = 4sin(2π3t + π)

Answer 1

Answer:

a. 4

b. 3

c. pi

Explanation:

Generic formula of a sine wave: s(t) = Amp * sin ( 2*pi*freq*t + phase)

where, Amp => Amplitude

freq => frequency

phase => phase

Given sine wave: s(t) = 4sin(2π3t + π)

Comparing it with the generic form , we can identify that :

a. Amplitude : 4

b. Frequency : 3

c. Phase : pi

Amplitude measures peak displacement from origin, Frequency is the number of cycles per second and phase is the relative positioning of the wave with respect to the origin.

Answer 2

Answer:

1) Amplitude = 4

2) Frequency  =$1Hz$

3) Initial phase = $\pi$

Explanation:

The general equation of wave is

$y(t)=Asin(\omega t+\phi )$

where

A is the amplitude of the wave

$\omega$ is the angular frequency of the wave

$\phi$ is the initial phase of the wave

The given wave function is

$s(t)=4sin(2\pi t+\pi )$

Comparing with the standard function we get

1) Amplitude = 4

2) Frequency  =$\frac{\omega }{2\pi }=\frac{2\pi }{2\pi }=1Hz$

3) Initial phase = $\pi$