Question

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

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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Answer #1

I got: #T=2pi#

Explanation:

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)=Asin(omegat)# Function of #t#

where in your case you have:

#y(x)=-3sin(1x)# 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).

#omega# is a number that tells you the "speed" of your wave in terms of radians per seconds or:

#omega=(2pi)/T# where #T# is the period.

In your case #omega=1# so that:
#(2pi)/T=1#
and
#T=2pi# so that the period will be #2pi#

We can "see" this wave graphically:
graph{-3sin(x) [-10, 10, -5, 5]}

answered by: Gió
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