A particular sound wave can be graphed using the function y=-3sinx, how do you find the period of the function?

Marcelo Mullins 2022-07-23 Answered
A particular sound wave can be graphed using the function y = 3 sin x, how do you find the period of the function?
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Answers (1)

LitikoIDu6
Answered 2022-07-24 Author has 10 answers
For the case of a sound wave I would prefer to "see" it as a displacement along y as function of time. In general the form of the wave would be:
y ( t ) = A sin ( ω t ) Function of t
where in your case you have:
y ( x ) = 3 sin ( 1 x ) Function of x
although this may seem a bit strange and difficult it allows you to "see" the various components of your wave:
A is the amplitude or the maximum reached by the displacement of your wave that in your case is 3 (the minus tells you that at the start the sine wave will be "upside down" compared to a normal sine).
ω is a number that tells you the "speed" of your wave in terms of radians per seconds or:
ω = 2 π T where T is the period.
In your case ω = 1 so that:
2 π T = 1
and
T = 2 π so that the period will be 2 π
We can "see" this wave graphically:
graph{ 3 sin ( x ) [ 10 , 10 , 5 , 5 ]}

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