I've been struggling in this sound wave question for more than 30min, can someone help me please?

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1 Answer
Sep 29, 2017

a. The period is 3
b. The amplitude is 1/4
c. Sorry, I wasn't able to explain clearly. Please help.

Explanation:

a. The period of trigonometric functions are as follows.
f(x) = sin(aθ) or f(x) = cos(aθ) -> The period is (2pi)/a
f(x) = tan(aθ) -> The period is (pi)/a

In the equation y=1/4cos((2pi)/3theta), a=(2pi)/3,
so the period is (2pi)/((2pi)/3)=3.

b. The amplitude is the maximum absolute value of the wave.
For sin or cos functions, the amplitude is the coefficient before
the trigonometrics.Therefore the amplitude for y=1/4cos((2pi)/3theta) is 1/4.

c. The equation of a function is a relationship between the variables.
For example, y=2x is an equation, and this means y is
proportional to x.

The equation y=1/4cos((2pi)/3theta) is a trigonometric function.
If you prot theta and y on a plane you will see a wave-shaped graph.