Question

Periodic Functions and Trigonometry.

A sound wave has a period of 0.02 seconds and an amplitude of 3 units. Sketch a graph of the sound wave.

Can you please show work so I understand how it is done, I am sure something like this will be on my test. I am having a lot of trouble with this unit.

Thanks!

Answer 1

http://www.wolframalpha.com/input/?i=3*sin%282*pi*%281%2F0.02%29*t%29

Answer 2

The general form for sinusoidal motion is amplitude*sin(2*pi*f*t) where f is frequency. Frequency is the multiplicative inverse of the period.

Answer 3

period -0.02 seconds per cycle
frequency - 50 cycle per seconds
angular frequency - 100pi
3cos(100pi(t)+theta)

Answer 4

When sketching this, the period is the length of a full cycle. So you draw your x-y coordinate from 0 to 0.02. You now need to find the increment. The increment is 1/4 of the period. In other words, divide 0.02 by 4 and you get 0.005. So you scratch on your line 0.005 (Four increments, fourth increment ending at 0.02. The amplitude means you go up three and go down three. These are some odd numbers but try to follow this on the map provided above by linjaaho, but note that he has two cycles from -0.02 to 0 and from 0 to 0.02; what I describe here is from 0 to 0.002. Good luck.