A particular sound wave can be graphed using the function y = − 3 sin ⁡ x, how do you find the period of the function?

Question

A particular sound wave can be graphed using the function   y  =  −  3  sin  ⁡  x, how do you find the period of the function?

LitikoIDu6 · Accepted Answer

For the case of a sound wave I would prefer to &quot;see&quot; 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 twhere in your case you have:  y  (  x  )  =  −  3  sin  ⁡  (  1  x  ) Function of xalthough this may seem a bit strange and difficult it allows you to &quot;see&quot; 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 &quot;upside down&quot; compared to a normal sine).  ω is a number that tells you the &quot;speed&quot; 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    =  1and  T  =  2  π so that the period will be   2  πWe can &quot;see&quot; this wave graphically:graph{  −  3  sin  ⁡  (  x  )  [  −  10  ,  10  ,  −  5  ,  5  ]}

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

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