Hi there! Can you take couple minutes to help me out with a sound wave question please? Thanks!

a. The period is how long the cycle of a wave is, the unit length between two adjacent peaks/troughs.

So, we want to know what values for #x# will give these peaks. We know that the maximum value of #cos(a)=1# and occurs when #a=n2pi, ninZZ#

So, we know that a peak will occur when #a=0, +-2pi, +-4pi, etc.#

#(2pi)/3x=0#
#x=0#

#(2pi)/3x=2pi#
#x/3=1#
#x=3#

The unit length between two peaks is the period and is 3.

For period I say it is unit length, which is the number of whole squares on the graph.

b. The amplitude is the highest point reached by the graph from the equilibrium point. This can be found using the equation as the maximum value for #cos((2pi)/3x# is 1, so #1/4*1=1/4#

c. The midline is the line that runs through the equilibrium point of the graph, where the "average" #y# value is, or the line which the graph oscillates around.

Since the graph has a maximum of 1 and a minimum of -1, the midline is found by doing #(y_"max"+y_"min")/2#, #(1-1)/2=0/2=0#. Therefore the midline is at #y=0#

Also, as the general equation is in the form of #y=acos(bx)+c#, the value of #c# gives the value of the midline, and since #c=0# the midline is #y=0#